Daily Papers

The paradigm of agentic AI is shifting from engineered complex workflows to post-training native models. However, existing agents are typically confined to static, predefined action spaces--such as exclusively using APIs, GUI events, or robotic commands. This rigidity limits their adaptability in dynamic environments where the optimal granularity of interaction varies contextually. To bridge this gap, we propose CrossAgent, a unified agentic model that masters heterogeneous action spaces and autonomously selects the most effective interface for each step of a trajectory. We introduce a comprehensive training pipeline that integrates cold-start supervised fine-tuning with a Multi-Turn Group Relative Policy Optimization (GRPO) algorithm. This approach enables the agent to learn adaptive action switching--balancing high-level efficiency with low-level precision--without human-specified rules. Extensive experiments on over 800 tasks in the open-world Minecraft environment demonstrate that CrossAgent achieves state-of-the-art performance. By dynamically leveraging the strengths of diverse action spaces, our model significantly outperforms fixed-action baselines, exhibiting superior generalization and efficiency in long-horizon reasoning. All code and models are available at https://github.com/CraftJarvis/OpenHA

Training Large Language Models (LLMs) for multi-turn Tool-Integrated Reasoning (TIR) - where models iteratively reason, generate code, and verify through execution - remains challenging for existing reinforcement learning (RL) approaches. Current RL methods, exemplified by Group Relative Policy Optimization (GRPO), suffer from coarse-grained, trajectory-level rewards that provide insufficient learning signals for complex multi-turn interactions, leading to training stagnation. To address this issue, we propose Group Turn Policy Optimization (GTPO), a novel RL algorithm specifically designed for training LLMs on multi-turn TIR tasks. GTPO introduces three key innovations: (1) turn-level reward assignment that provides fine-grained feedback for individual turns, (2) return-based advantage estimation where normalized discounted returns are calculated as advantages, and (3) self-supervised reward shaping that exploits self-supervision signals from generated code to densify sparse binary outcome-based rewards. Our comprehensive evaluation demonstrates that GTPO outperforms GRPO by 3.0% on average across diverse reasoning benchmarks, establishing its effectiveness for advancing complex mathematical reasoning in the real world.

Reinforcement learning (RL) has re-emerged as a natural approach for training interactive LLM agents in real-world environments. However, directly applying the widely used Group Relative Policy Optimization (GRPO) algorithm to multi-turn tasks exposes notable limitations, particularly in scenarios requiring long-horizon reasoning. To address these challenges, we investigate more stable and effective advantage estimation strategies, especially for multi-turn settings. We first explore Proximal Policy Optimization (PPO) as an alternative and find it to be more robust than GRPO. To further enhance PPO in multi-turn scenarios, we introduce turn-PPO, a variant that operates on a turn-level MDP formulation, as opposed to the commonly used token-level MDP. Our results on the WebShop and Sokoban datasets demonstrate the effectiveness of turn-PPO, both with and without long reasoning components.

A large amount of work has been done in Multi-Agent Systems (MAS) for modeling and solving problems with multiple interacting agents. However, most LLMs are pretrained independently and not specifically optimized for coordination. Existing LLM fine-tuning frameworks rely on individual rewards, which require complex reward designs for each agent to encourage collaboration. To address these challenges, we model LLM collaboration as a cooperative Multi-Agent Reinforcement Learning (MARL) problem. We develop a multi-agent, multi-turn algorithm, Multi-Agent Group Relative Policy Optimization (MAGRPO), to solve it, building on current RL approaches for LLMs as well as MARL techniques. Our experiments on LLM writing and coding collaboration demonstrate that fine-tuning MAS with MAGRPO enables agents to generate high-quality responses efficiently through effective cooperation. Our approach opens the door to using other MARL methods for LLMs and highlights the associated challenges.

Multi-agent systems perform well on general reasoning tasks. However, the lack of training in specialized areas hinders their accuracy. Current training methods train a unified large language model (LLM) for all agents in the system. This may limit the performances due to different distributions underlying for different agents. Therefore, training multi-agent systems with distinct LLMs should be the next step to solve. However, this approach introduces optimization challenges. For example, agents operate at different frequencies, rollouts involve varying sub-agent invocations, and agents are often deployed across separate servers, disrupting end-to-end gradient flow. To address these issues, we propose M-GRPO, a hierarchical extension of Group Relative Policy Optimization designed for vertical Multi-agent systems with a main agent (planner) and multiple sub-agents (multi-turn tool executors). M-GRPO computes group-relative advantages for both main and sub-agents, maintaining hierarchical credit assignment. It also introduces a trajectory-alignment scheme that generates fixed-size batches despite variable sub-agent invocations. We deploy a decoupled training pipeline in which agents run on separate servers and exchange minimal statistics via a shared store. This enables scalable training without cross-server backpropagation. In experiments on real-world benchmarks (e.g., GAIA, XBench-DeepSearch, and WebWalkerQA), M-GRPO consistently outperforms both single-agent GRPO and multi-agent GRPO with frozen sub-agents, demonstrating improved stability and sample efficiency. These results show that aligning heterogeneous trajectories and decoupling optimization across specialized agents enhances tool-augmented reasoning tasks.

We revisit Group Relative Policy Optimization (GRPO) in both on-policy and off-policy optimization regimes. Our motivation comes from recent work on off-policy Proximal Policy Optimization (PPO), which improves training stability, sampling efficiency, and memory usage. In addition, a recent analysis of GRPO suggests that estimating the advantage function with off-policy samples could be beneficial. Building on these observations, we adapt GRPO to the off-policy setting. We show that both on-policy and off-policy GRPO objectives yield an improvement in the reward. This result motivates the use of clipped surrogate objectives in the off-policy version of GRPO. We then compare the empirical performance of reinforcement learning with verifiable rewards in post-training using both GRPO variants. Our results show that off-policy GRPO either significantly outperforms or performs on par with its on-policy counterpart.

Group Relative Policy Optimization (GRPO) is a prominent reinforcement learning algorithm for post-training Large Language Models (LLMs). It is commonly believed that GRPO necessitates a large group size to ensure stable training via precise statistical estimation, which incurs substantial computational overhead. In this work, we challenge this assumption by reframing GRPO as a form of contrastive learning, which reveals a fundamental connection to Direct Preference Optimization (DPO). Motivated by DPO's empirical success, we investigate the minimal two-rollout case (2-GRPO), a configuration previously deemed infeasible. We provide a rigorous theoretical analysis to validate 2-GRPO and demonstrate empirically that it achieves performance on par with 16-GRPO, despite using only 1/8 of the rollouts and reducing training time by over 70%.

Recent advances in reinforcement learning (RL) have significantly enhanced the reasoning capabilities of large language models (LLMs). Group Relative Policy Optimization (GRPO), a lightweight variant of Proximal Policy Optimization (PPO), improves efficiency but suffers from limited exploration and training instability, limiting its effectiveness on complex reasoning tasks. To address these challenges, we introduce EFRame, an Exploration-Filter-Replay framework that augments GRPO across three dimensions: additional rollouts enable deeper and more targeted exploration, online filtering removes low-quality samples to stabilize gradients and accelerate training, and experience replay amplifies rare yet informative trajectories for stable convergence. This unified framework establishes a principled training cycle that balances exploration, efficiency, and stability. Experiments on diverse reasoning benchmarks demonstrate that EFRame achieves consistent gains, including a 37.9\% relative improvement on Geometry3K over GRPO. EFRame further supports fine-grained sample categorization and precise entropy control, highlighting it as a robust solution for advancing deeper reasoning in LLMs. Our code is available at https://github.com/597358816/EFRame.

Large Language Models (LLMs) perform well in language tasks but often lack collaborative awareness and struggle to optimize global performance in multi-agent settings. We present a reinforcement learning-augmented LLM agent framework that formulates cooperation as a decentralized partially observable Markov decision process (Dec-POMDP) and adopts centralized training with decentralized execution (CTDE). We introduce Group Relative Policy Optimization (GRPO) to jointly optimize agent policies with access to global signals during training, together with a simplified joint reward that balances task quality, speed, and coordination cost. On collaborative writing and coding benchmarks, our framework delivers a 3x increase in task processing speed over single-agent baselines, 98.7% structural/style consistency in writing, and a 74.6% test pass rate in coding. The approach consistently outperforms strong multi-agent LLM baselines and provides a practical path toward reliable collaboration in complex workflows.

This paper investigates approaches to enhance the reasoning capabilities of Large Language Model (LLM) agents using Reinforcement Learning (RL). Specifically, we focus on multi-turn tool-use scenarios, which can be naturally modeled as Markov Decision Processes (MDPs). While existing approaches often train multi-turn LLM agents with trajectory-level advantage estimation in bandit settings, they struggle with turn-level credit assignment across multiple decision steps, limiting their performance on multi-turn reasoning tasks. To address this, we introduce a fine-grained turn-level advantage estimation strategy to enable more precise credit assignment in multi-turn agent interactions. The strategy is general and can be incorporated into various RL algorithms such as Group Relative Preference Optimization (GRPO). Our experimental evaluation on multi-turn reasoning and search-based tool-use tasks with GRPO implementations highlights the effectiveness of the MDP framework and the turn-level credit assignment in advancing the multi-turn reasoning capabilities of LLM agents in complex decision-making settings. Our method achieves 100% success in tool execution and 50% accuracy in exact answer matching, significantly outperforming baselines, which fail to invoke tools and achieve only 20-30% exact match accuracy.

Tool-integrated (TI) reinforcement learning (RL) enables large language models (LLMs) to perform multi-step reasoning by interacting with external tools such as search engines and retrievers. Group Relative Policy Optimization (GRPO), exemplified by the recent Search-R1, offers fast convergence and a value-free formulation that makes it appealing for this setting, yet consistently suffers from training collapse. We identify Lazy Likelihood Displacement (LLD), a systematic reduction or stagnation in the likelihood of both correct and incorrect responses, as the core mechanism driving this failure. LLD emerges early and triggers a self-reinforcing LLD Death Spiral, where declining likelihood leads to low-confidence responses, inflating gradients, and ultimately causing collapse. We empirically characterize this process across models on a Search-R1-style, search-integrated question answering task, revealing a consistent three-phase trajectory: early stagnation, steady decay, and accelerated collapse. To address this, we propose a lightweight likelihood-preserving regularization LLDS for GRPO that activates only when a trajectory's likelihood decreases, and regularizes only the tokens responsible. This fine-grained structure mitigates LLD with minimal interference to optimization. Across seven open-domain and multi-hop QA benchmarks, our method stabilizes training, prevents gradient explosion, and yields substantial performance improvements, including +37.8% gains on Qwen2.5-3B and +32.0% gains on Qwen2.5-7B. Our results establish LLD as a fundamental bottleneck in GRPO-based TIRL and provide a practical path toward stable, scalable training of tool-integrated LLM.

Recent advances in reinforcement learning (RL) have significantly enhanced the agentic capabilities of large language models (LLMs). In long-term and multi-turn agent tasks, existing approaches driven solely by outcome rewards often suffer from the problem of sparse supervision. To address the challenge, we propose Tree-based Group Relative Policy Optimization (Tree-GRPO), a grouped agent RL method based on tree search, where each tree node represents the complete agent interaction step. By sharing common prefixes, the tree search sampling increases the number of rollouts achievable within a fixed budget of tokens or tool calls. Moreover, we find that the tree-structured trajectory naturally allows the construction of step-wise process supervised signals even using only the outcome reward. Based on this, Tree-GRPO estimates the grouped relative advantages both on intra-tree and inter-tree levels. Through theoretical analysis, we demonstrate that the objective of intra-tree level group relative policy optimization is equivalent to that of step-level direct preference learning. Experiments across 11 datasets and 3 types of QA tasks demonstrate the superiority of the proposed tree-based RL over the chain-based RL method.

Recent advances in motion planning for autonomous driving have led to models capable of generating high-quality trajectories. However, most existing planners tend to fix their policy after supervised training, leading to consistent but rigid driving behaviors. This limits their ability to reflect human preferences or adapt to dynamic, instruction-driven demands. In this work, we propose a diffusion-based multi-head trajectory planner(M-diffusion planner). During the early training stage, all output heads share weights to learn to generate high-quality trajectories. Leveraging the probabilistic nature of diffusion models, we then apply Group Relative Policy Optimization (GRPO) to fine-tune the pre-trained model for diverse policy-specific behaviors. At inference time, we incorporate a large language model (LLM) to guide strategy selection, enabling dynamic, instruction-aware planning without switching models. Closed-loop simulation demonstrates that our post-trained planner retains strong planning capability while achieving state-of-the-art (SOTA) performance on the nuPlan val14 benchmark. Open-loop results further show that the generated trajectories exhibit clear diversity, effectively satisfying multi-modal driving behavior requirements. The code and related experiments will be released upon acceptance of the paper.

As language models become increasingly capable, users expect them to provide not only accurate responses but also behaviors aligned with diverse human preferences across a variety of scenarios. To achieve this, Reinforcement learning (RL) pipelines have begun incorporating multiple rewards, each capturing a distinct preference, to guide models toward these desired behaviors. However, recent work has defaulted to apply Group Relative Policy Optimization (GRPO) under multi-reward setting without examining its suitability. In this paper, we demonstrate that directly applying GRPO to normalize distinct rollout reward combinations causes them to collapse into identical advantage values, reducing the resolution of the training signal and resulting in suboptimal convergence and, in some cases, early training failure. We then introduce Group reward-Decoupled Normalization Policy Optimization (GDPO), a new policy optimization method to resolve these issues by decoupling the normalization of individual rewards, more faithfully preserving their relative differences and enabling more accurate multi-reward optimization, along with substantially improved training stability. We compare GDPO with GRPO across three tasks: tool calling, math reasoning, and coding reasoning, evaluating both correctness metrics (accuracy, bug ratio) and constraint adherence metrics (format, length). Across all settings, GDPO consistently outperforms GRPO, demonstrating its effectiveness and generalizability for multi-reward reinforcement learning optimization.

Visual generation is dominated by three paradigms: AutoRegressive (AR), diffusion, and Visual AutoRegressive (VAR) models. Unlike AR and diffusion, VARs operate on heterogeneous input structures across their generation steps, which creates severe asynchronous policy conflicts. This issue becomes particularly acute in reinforcement learning (RL) scenarios, leading to unstable training and suboptimal alignment. To resolve this, we propose a novel framework to enhance Group Relative Policy Optimization (GRPO) by explicitly managing these conflicts. Our method integrates three synergistic components: 1) a stabilizing intermediate reward to guide early-stage generation; 2) a dynamic time-step reweighting scheme for precise credit assignment; and 3) a novel mask propagation algorithm, derived from principles of Reward Feedback Learning (ReFL), designed to isolate optimization effects both spatially and temporally. Our approach demonstrates significant improvements in sample quality and objective alignment over the vanilla GRPO baseline, enabling robust and effective optimization for VAR models.

Recent advances in reasoning with large language models (LLMs) have shown the effectiveness of Monte Carlo Tree Search (MCTS) for generating high-quality intermediate trajectories, particularly in math and symbolic domains. Inspired by this, we explore how MCTS-derived trajectories, traditionally used for training value or reward models, can be repurposed to improve policy optimization in preference-based reinforcement learning (RL). Specifically, we focus on Group Relative Policy Optimization (GRPO), a recent algorithm that enables preference-consistent policy learning without value networks. We propose a staged GRPO training paradigm where completions are derived from partially revealed MCTS rollouts, introducing a novel tree-structured setting for advantage estimation. This leads to a rich class of prefix-conditioned reward signals, which we analyze theoretically and empirically. Our initial results indicate that while structured advantage estimation can stabilize updates and better reflect compositional reasoning quality, challenges such as advantage saturation and reward signal collapse remain. We propose heuristic and statistical solutions to mitigate these issues and discuss open challenges for learning under staged or tree-like reward structures.

LLM agents have emerged as powerful systems for tackling multi-turn tasks by interleaving internal reasoning and external tool interactions. Agentic Reinforcement Learning has recently drawn significant research attention as a critical post-training paradigm to further refine these capabilities. In this paper, we present AT^2PO (Agentic Turn-based Policy Optimization via Tree Search), a unified framework for multi-turn agentic RL that addresses three core challenges: limited exploration diversity, sparse credit assignment, and misaligned policy optimization. AT^2PO introduces a turn-level tree structure that jointly enables Entropy-Guided Tree Expansion for strategic exploration and Turn-wise Credit Assignment for fine-grained reward propagation from sparse outcomes. Complementing this, we propose Agentic Turn-based Policy Optimization, a turn-level learning objective that aligns policy updates with the natural decision granularity of agentic interactions. ATPO is orthogonal to tree search and can be readily integrated into any multi-turn RL pipeline. Experiments across seven benchmarks demonstrate consistent improvements over the state-of-the-art baseline by up to 1.84 percentage points in average, with ablation studies validating the effectiveness of each component. Our code is available at https://github.com/zzfoutofspace/ATPO.

Group Relative Policy Optimization (GRPO) has proven to be an effective tool for post-training language models (LMs). However, AI systems are increasingly expressed as modular programs that mix together multiple LM calls with distinct prompt templates and other tools, and it is not clear how best to leverage GRPO to improve these systems. We begin to address this challenge by defining mmGRPO, a simple multi-module generalization of GRPO that groups LM calls by module across rollouts and handles variable-length and interrupted trajectories. We find that mmGRPO, composed with automatic prompt optimization, improves accuracy by 11% on average across classification, many-hop search, and privacy-preserving delegation tasks against the post-trained LM, and by 5% against prompt optimization on its own. We open-source mmGRPO in DSPy as the dspy.GRPO optimizer.

Reinforcement learning (RL) is vital for optimizing large language models (LLMs). Recent Group Relative Policy Optimization (GRPO) estimates advantages using multiple on-policy outputs per prompt, leading to high computational costs and low data efficiency. To address this, we introduce Replay-Enhanced Policy Optimization (RePO), which leverages diverse replay strategies to retrieve off-policy samples from a replay buffer, allowing policy optimization based on a broader and more diverse set of samples for each prompt. Experiments on five LLMs across seven mathematical reasoning benchmarks demonstrate that RePO achieves absolute average performance gains of 18.4 and 4.1 points for Qwen2.5-Math-1.5B and Qwen3-1.7B, respectively, compared to GRPO. Further analysis indicates that RePO increases computational cost by 15% while raising the number of effective optimization steps by 48% for Qwen3-1.7B, with both on-policy and off-policy sample numbers set to 8. The repository can be accessed at https://github.com/SihengLi99/RePO.

The evolution of Large Language Models (LLMs) has catalyzed a paradigm shift from superficial instruction following to rigorous long-horizon reasoning. While Group Relative Policy Optimization (GRPO) has emerged as a pivotal mechanism for eliciting such post-training reasoning capabilities due to its exceptional performance, it remains plagued by significant training instability and poor sample efficiency. We theoretically identify the root cause of these issues as the lack of distinctiveness within on-policy rollouts: for routine queries, highly homogeneous samples induce destructive gradient conflicts; whereas for hard queries, the scarcity of valid positive samples results in ineffective optimization. To bridge this gap, we propose Distinctiveness-aware Group Relative Policy Optimization (DaGRPO). DaGRPO incorporates two core mechanisms: (1) Sequence-level Gradient Rectification, which utilizes fine-grained scoring to dynamically mask sample pairs with low distinctiveness, thereby eradicating gradient conflicts at the source; and (2) Off-policy Data Augmentation, which introduces high-quality anchors to recover training signals for challenging tasks. Extensive experiments across 9 mathematical reasoning and out-of-distribution (OOD) generalization benchmarks demonstrate that DaGRPO significantly surpasses existing SFT, GRPO, and hybrid baselines, achieving new state-of-the-art performance (e.g., a +4.7% average accuracy gain on math benchmarks). Furthermore, in-depth analysis confirms that DaGRPO effectively mitigates gradient explosion and accelerates the emergence of long-chain reasoning capabilities.

Generative Reward Models (GRMs) have attracted considerable research interest in reward modeling due to their interpretability, inference-time scalability, and potential for refinement through reinforcement learning (RL). However, widely used pairwise GRMs create a computational bottleneck when integrated with RL algorithms such as Group Relative Policy Optimization (GRPO). This bottleneck arises from two factors: (i) the O(n^2) time complexity of pairwise comparisons required to obtain relative scores, and (ii) the computational overhead of repeated sampling or additional chain-of-thought (CoT) reasoning to improve performance. To address the first factor, we propose Intergroup Relative Preference Optimization (IRPO), a novel RL framework that incorporates the well-established Bradley-Terry model into GRPO. By generating a pointwise score for each response, IRPO enables efficient evaluation of arbitrarily many candidates during RL training while preserving interpretability and fine-grained reward signals. Experimental results demonstrate that IRPO achieves state-of-the-art (SOTA) performance among pointwise GRMs across multiple benchmarks, with performance comparable to that of current leading pairwise GRMs. Furthermore, we show that IRPO significantly outperforms pairwise GRMs in post-training evaluations.

Large Language Model (LLM)-driven Multi-agent systems (Mas) have recently emerged as a powerful paradigm for tackling complex real-world tasks. However, existing Mas construction methods typically rely on manually crafted interaction mechanisms or heuristic rules, introducing human biases and constraining the autonomous ability. Even with recent advances in adaptive Mas construction, existing systems largely remain within the paradigm of semi-autonomous patterns. In this work, we propose MasHost, a Reinforcement Learning (RL)-based framework for autonomous and query-adaptive Mas design. By formulating Mas construction as a graph search problem, our proposed MasHost jointly samples agent roles and their interactions through a unified probabilistic sampling mechanism. Beyond the accuracy and efficiency objectives pursued in prior works, we introduce component rationality as an additional and novel design principle in Mas. To achieve this multi-objective optimization, we propose Hierarchical Relative Policy Optimization (HRPO), a novel RL strategy that collaboratively integrates group-relative advantages and action-wise rewards. To our knowledge, our proposed MasHost is the first RL-driven framework for autonomous Mas graph construction. Extensive experiments on six benchmarks demonstrate that MasHost consistently outperforms most competitive baselines, validating its effectiveness, efficiency, and structure rationality.

Reinforcement learning has been widely applied to enhance the reasoning capabilities of large language models. Extending the inference limits of smaller models has become a prominent research focus. However, algorithms such as Group Relative Policy Optimization (GRPO) suffer from a clear drawback: the upper bound of a model's rollout responses is entirely determined by the model itself, preventing the acquisition of knowledge from samples that are either all incorrect or all correct. In this paper, we introduce Group Contrastive Policy Optimization (GCPO), a method that incorporates external standard reference answers. When the model cannot solve a problem, the reference answer supplies the correct response, steering the model toward an unequivocally accurate update direction. This approach offers two main advantages: (1) it improves training efficiency by fully utilizing every sample; (2) it enables the model to emulate the problem solving strategy of the reference answer during training, thereby enhancing generalization in reasoning. GCPO achieves outstanding results across multiple benchmark datasets, yielding substantial improvements over the baseline model. Our code is available at: https://github.com/AchoWu/GCPO.

Large Language Models (LLMs) have made remarkable progress in enhancing step-by-step reasoning through reinforcement learning. However, the Group Relative Policy Optimization (GRPO) algorithm, which relies on sparse reward rules, often encounters the issue of identical rewards within groups, leading to the advantage collapse problem. Existing works typically address this challenge from two perspectives: enforcing model reflection to enhance response diversity, and introducing internal feedback to augment the training signal (advantage). In this work, we begin by analyzing the limitations of model reflection and investigating the policy entropy of responses at the fine-grained sample level. Based on our experimental findings, we propose the EDGE-GRPO algorithm, which adopts Entropy-Driven Advantage and Guided Error Correction to effectively mitigate the problem of advantage collapse. Extensive experiments on several main reasoning benchmarks demonstrate the effectiveness and superiority of our approach. It is available at https://github.com/ZhangXJ199/EDGE-GRPO.

Reinforcement Learning (RL) has proven to be an effective post-training strategy for enhancing reasoning in vision-language models (VLMs). Group Relative Policy Optimization (GRPO) is a recent prominent method that encourages models to generate complete reasoning traces before answering, leading to increased token usage and computational cost. Inspired by the human-like thinking process-where people skip reasoning for easy questions but think carefully when needed-we explore how to enable VLMs to first decide when reasoning is necessary. To realize this, we propose TON, a two-stage training strategy: (i) a supervised fine-tuning (SFT) stage with a simple yet effective 'thought dropout' operation, where reasoning traces are randomly replaced with empty thoughts. This introduces a think-or-not format that serves as a cold start for selective reasoning; (ii) a GRPO stage that enables the model to freely explore when to think or not, while maximizing task-aware outcome rewards. Experimental results show that TON can reduce the completion length by up to 90% compared to vanilla GRPO, without sacrificing performance or even improving it. Further evaluations across diverse vision-language tasks-covering a range of reasoning difficulties under both 3B and 7B models-consistently reveal that the model progressively learns to bypass unnecessary reasoning steps as training advances. These findings shed light on the path toward human-like reasoning patterns in reinforcement learning approaches. Our code is available at https://github.com/kokolerk/TON.

Large multimodal reasoning models have achieved rapid progress, but their advancement is constrained by two major limitations: the absence of open, large-scale, high-quality long chain-of-thought (CoT) data, and the instability of reinforcement learning (RL) algorithms in post-training. Group Relative Policy Optimization (GRPO), the standard framework for RL fine-tuning, is prone to gradient vanishing when reward variance is low, which weakens optimization signals and impairs convergence. This work makes three contributions: (1) We propose Variance-Aware Sampling (VAS), a data selection strategy guided by Variance Promotion Score (VPS) that combines outcome variance and trajectory diversity to promote reward variance and stabilize policy optimization. (2) We release large-scale, carefully curated resources containing ~1.6M long CoT cold-start data and ~15k RL QA pairs, designed to ensure quality, difficulty, and diversity, along with a fully reproducible end-to-end training codebase. (3) We open-source a family of multimodal reasoning models in multiple scales, establishing standardized baselines for the community. Experiments across mathematical reasoning benchmarks demonstrate the effectiveness of both the curated data and the proposed VAS. Comprehensive ablation studies and analyses provide further insight into the contributions of each component. In addition, we theoretically establish that reward variance lower-bounds the expected policy gradient magnitude, with VAS serving as a practical mechanism to realize this guarantee. Our code, data, and checkpoints are available at https://github.com/LengSicong/MMR1.

Group Relative Policy Optimization (GRPO) enhances policy learning by computing gradients from relative comparisons among candidate outputs that share a common input prefix. Despite its effectiveness, GRPO introduces substantial computational overhead when processing long shared prefixes, which must be redundantly encoded for each group member. This inefficiency becomes a major scalability bottleneck in long-context learning scenarios. We propose Prefix Grouper, an efficient GRPO training algorithm that eliminates redundant prefix computation via a Shared-Prefix Forward strategy. In particular, by restructuring self-attention into two parts, our method enables the shared prefix to be encoded only once, while preserving full differentiability and compatibility with end-to-end training. We provide both theoretical and empirical evidence that Prefix Grouper is training-equivalent to standard GRPO: it yields identical forward outputs and backward gradients, ensuring that the optimization dynamics and final policy performance remain unchanged. Empirically, our experiments confirm that Prefix Grouper achieves consistent results while significantly reducing the computational cost of training, particularly in long-prefix scenarios. The proposed method is fully plug-and-play: it is compatible with existing GRPO-based architectures and can be seamlessly integrated into current training pipelines as a drop-in replacement, requiring no structural modifications and only minimal changes to input construction and attention computation. Prefix Grouper enables the use of larger group sizes under the same computational budget, thereby improving the scalability of GRPO to more complex tasks and larger models. Code is now available at https://github.com/johncaged/PrefixGrouper

Group-Relative Policy Optimization (GRPO) is a key technique for training large reasoning models, yet it suffers from a critical vulnerability: the Think-Answer Mismatch, where noisy reward signals corrupt the learning process. This problem is most severe in unbalanced response groups, paradoxically degrading the signal precisely when it should be most informative. To address this challenge, we propose Stable Group-Relative Policy Optimization (S-GRPO), a principled enhancement that derives optimal, noise-aware advantage weights to stabilize training. Our comprehensive experiments on mathematical reasoning benchmarks demonstrate S-GRPO's effectiveness and robustness. On various models, S-GRPO significantly outperforms DR. GRPO, achieving performance gains of +2.5% on Qwen-Math-7B-Base, +2.2% on Llama-3.2-3B-Base, and +2.4% on Qwen-Math-1.5B-Instruct. Most critically, while standard GRPO fails to learn under 20% synthetic reward noise, S-GRPO maintains stable learning progress. These results highlight S-GRPO's potential for more robust and effective training of large-scale reasoning models. \footnote{Code and data are available at: https://github.com/shenpeijun0212/S-GRPO

Recent works have demonstrated the effectiveness of reinforcement learning (RL)-based post-training in enhancing the reasoning capabilities of large language models (LLMs). In particular, Group Relative Policy Optimization (GRPO) has shown impressive success by employing a PPO-style reinforcement algorithm with group-based normalized rewards. However, the application of GRPO to Video Large Language Models (Video LLMs) has been less studied. In this paper, we explore GRPO for video LLMs and identify two primary issues that impede its effective learning: (1) reliance on safeguards, and (2) the vanishing advantage problem. To mitigate these challenges, we propose DeepVideo-R1, a video large language model trained with our proposed Reg-GRPO (Regressive GRPO) and difficulty-aware data augmentation strategy. Reg-GRPO reformulates the GRPO objective as a regression task, directly predicting the advantage in GRPO. This design eliminates the need for safeguards like clipping and min functions, thereby facilitating more direct policy guidance by aligning the model with the advantage values. We also design the difficulty-aware data augmentation strategy that dynamically augments training samples at solvable difficulty levels, fostering diverse and informative reward signals. Our comprehensive experiments show that DeepVideo-R1 significantly improves video reasoning performance across multiple video reasoning benchmarks.

Group Relative Policy Optimization (GRPO) has emerged as a powerful reinforcement learning paradigm for post-training video generation models. However, existing GRPO pipelines rely on static, fixed-capacity reward models whose evaluation behavior is frozen during training. Such rigid rewards introduce distributional bias, saturate quickly as the generator improves, and ultimately limit the stability and effectiveness of reinforcement-based alignment. We propose Self-Paced GRPO, a competence-aware GRPO framework in which reward feedback co-evolves with the generator. Our method introduces a progressive reward mechanism that automatically shifts its emphasis from coarse visual fidelity to temporal coherence and fine-grained text-video semantic alignment as generation quality increases. This self-paced curriculum alleviates reward-policy mismatch, mitigates reward exploitation, and yields more stable optimization. Experiments on VBench across multiple video generation backbones demonstrate consistent improvements in both visual quality and semantic alignment over GRPO baselines with static rewards, validating the effectiveness and generality of Self-Paced GRPO.

Outcome-driven reinforcement learning has advanced reasoning in large language models (LLMs), but prevailing tool-augmented approaches train a single, monolithic policy that interleaves thoughts and tool calls under full context; this scales poorly with long horizons and diverse tools and generalizes weakly to new scenarios. Agentic systems offer a promising alternative by decomposing work across specialized modules, yet most remain training-free or rely on offline training decoupled from the live dynamics of multi-turn interaction. We introduce AgentFlow, a trainable, in-the-flow agentic framework that coordinates four modules (planner, executor, verifier, generator) through an evolving memory and directly optimizes its planner inside the multi-turn loop. To train on-policy in live environments, we propose Flow-based Group Refined Policy Optimization (Flow-GRPO), which tackles long-horizon, sparse-reward credit assignment by converting multi-turn optimization into a sequence of tractable single-turn policy updates. It broadcasts a single, verifiable trajectory-level outcome to every turn to align local planner decisions with global success and stabilizes learning with group-normalized advantages. Across ten benchmarks, AgentFlow with a 7B-scale backbone outperforms top-performing baselines with average accuracy gains of 14.9% on search, 14.0% on agentic, 14.5% on mathematical, and 4.1% on scientific tasks, even surpassing larger proprietary models like GPT-4o. Further analyses confirm the benefits of in-the-flow optimization, showing improved planning, enhanced tool-calling reliability, and positive scaling with model size and reasoning turns.

The exploration-exploitation (EE) trade-off is a central challenge in reinforcement learning (RL) for large language models (LLMs). With Group Relative Policy Optimization (GRPO), training tends to be exploitation driven: entropy decreases monotonically, samples convergence, and exploration fades. Most existing fixes are sample-centric: they seek or bonus rare samples, assuming exploration comes from novel trajectories and tokens. These heuristics depend on the "luck" of informative samples, lack principled control of the policy, and often yield limited or inconsistent gains. In this work, we are the first to introduce a distribution-centric perspective for RL, in which exploration is always guided by a "better" target distribution, and reveal that a policy's ability to resist entropy collapse is governed by the distribution itself rather than individual samples. Building on this insight, we propose Distribution-Centric Policy Optimization (DCPO), which reformulates entropy regulation as distribution-level regularization. DCPO achieves controllable entropy fully on-policy without sampling from external distributions, enabling efficient exploration while maintaining training stability. Across multiple models and seven benchmarks, DCPO improves over GRPO by about 20\% on average. Overall, DCPO replaces sample-level heuristics with distribution-level principles, offering a theoretically grounded and flexible framework for controllable exploration and a stronger EE trade-off. The code is available in https://github.com/597358816/DCPO.

Speech Recognition has seen a dramatic shift towards adopting Large Language Models (LLMs). This shift is partly driven by good scalability properties demonstrated by LLMs, ability to leverage large amounts of labelled, unlabelled speech and text data, streaming capabilities with auto-regressive framework and multi-tasking with instruction following characteristics of LLMs. However, simple next-token prediction objective, typically employed with LLMs, have certain limitations in performance and challenges with hallucinations. In this paper, we propose application of Group Relative Policy Optimization (GRPO) to enable reinforcement learning from human feedback for automatic speech recognition (ASR). We design simple rule based reward functions to guide the policy updates. We demonstrate significant improvements in word error rate (upto 18.4% relative), reduction in hallucinations, increased robustness on out-of-domain datasets and effectiveness in domain adaptation.

Recent advances in group-based reinforcement learning (RL) have driven frontier large language models (LLMs) in single-turn tasks like mathematical reasoning. However, their scalability to long-horizon LLM agent training remains limited. Unlike static tasks, agent-environment interactions unfold over many steps and often yield sparse or delayed rewards, making credit assignment across individual steps significantly more challenging. In this work, we propose Group-in-Group Policy Optimization (GiGPO), a novel RL algorithm that achieves fine-grained credit assignment for LLM agents while preserving the appealing properties of group-based RL: critic-free, low memory, and stable convergence. GiGPO introduces a two-level structure for estimating relative advantage: (i) At the episode-level, GiGPO computes macro relative advantages based on groups of complete trajectories; (ii) At the step-level, GiGPO introduces an anchor state grouping mechanism that retroactively constructs step-level groups by identifying repeated environment states across trajectories. Actions stemming from the same state are grouped together, enabling micro relative advantage estimation. This hierarchical structure effectively captures both global trajectory quality and local step effectiveness without relying on auxiliary models or additional rollouts. We evaluate GiGPO on two challenging agent benchmarks, ALFWorld and WebShop, using Qwen2.5-1.5B-Instruct and Qwen2.5-7B-Instruct. Crucially, GiGPO delivers fine-grained per-step credit signals and achieves performance gains of > 12\% on ALFWorld and > 9\% on WebShop over the GRPO baseline: all while maintaining the same GPU memory overhead, identical LLM rollout, and incurring little to no additional time cost.

Group Relative Policy Optimization (GRPO) has demonstrated great utilization in post-training of Large Language Models (LLMs). In GRPO, prompts are answered by the model and, through reinforcement learning, preferred completions are learnt. Owing to the small communication volume, GRPO is inherently suitable for decentralised training as the prompts can be concurrently answered by multiple nodes and then exchanged in the forms of strings. In this work, we present the first adversarial attack in decentralised GRPO. We demonstrate that malicious parties can poison such systems by injecting arbitrary malicious tokens in benign models in both out-of-context and in-context attacks. Using empirical examples of math and coding tasks, we show that adversarial attacks can easily poison the benign nodes, polluting their local LLM post-training, achieving attack success rates up to 100% in as few as 50 iterations. We propose two ways to defend against these attacks, depending on whether all users train the same model or different models. We show that these defenses can achieve stop rates of up to 100%, making the attack impossible.

Aligning large language models (LLMs) with human values and safety constraints is challenging, especially when objectives like helpfulness, truthfulness, and avoidance of harm conflict. Reinforcement Learning from Human Feedback (RLHF) has achieved notable success in steering models, but is complex and can be unstable. Recent approaches such as Direct Preference Optimization (DPO) simplify preference-based fine-tuning but may introduce bias or trade-off certain objectives~dpo. In this work, we propose a Group Relative Policy Optimization (GRPO) framework with a multi-label reward regression model to achieve safe and aligned language generation. The GRPO algorithm optimizes a policy by comparing groups of sampled responses, eliminating the need for a separate value critic and improving training efficiency~grpo. We train a reward model to predict multiple alignment scores (e.g., safety, helpfulness, etc.), which are combined into a single reward signal. We provide a theoretical derivation for using this learned multi-aspect reward within GRPO and discuss its advantages and limitations. Empirically, our approach improves all the safety and quality metrics evaluated in language generation tasks on model scales (0.5B, 7B, and 14B parameters), demonstrating a robust balance of objectives. We compare GRPO to PPO-based RLHF and DPO, highlighting that GRPO achieves alignment with significantly lower computational cost and explicit multi-objective handling. \textbf{We will open-source all trained models at https://huggingface.co/hydroxai.

Reinforcement learning (RL) has demonstrated significant success in enhancing reasoning capabilities in large language models (LLMs). One of the most widely used RL methods is Group Relative Policy Optimization (GRPO)~Shao-2024-Deepseekmath, known for its memory efficiency and success in training DeepSeek-R1~Guo-2025-Deepseek. However, GRPO stalls when all sampled responses in a group are incorrect -- referred to as an all-negative-sample group -- as it fails to update the policy, hindering learning progress. The contributions of this paper are two-fold. First, we propose a simple yet effective framework that introduces response diversity within all-negative-sample groups in GRPO using AI feedback. We also provide a theoretical analysis, via a stylized model, showing how this diversification improves learning dynamics. Second, we empirically validate our approach, showing the improved performance across various model sizes (7B, 14B, 32B) in both offline and online learning settings with 10 benchmarks, including base and distilled variants. Our findings highlight that learning from all-negative-sample groups is not only feasible but beneficial, advancing recent insights from Xiong-2025-Minimalist.

Large language models (LLMs) have achieved impressive reasoning performance, with reinforcement learning with verifiable rewards (RLVR) emerging as a standard paradigm for post-training. A representative algorithm, group relative policy optimization (GRPO) (Shao et al., 2024), computes advantages by normalizing outcome rewards within response groups, but suffers from a vanishing advantage issue when all responses in a group receive identical rewards. To address this issue, we propose Adaptive Rollout and Response Reuse Policy Optimization (AR3PO), a sampling efficient RLVR algorithm that introduces two novel techniques: adaptive rollout, which dynamically allocates more responses to difficult prompts while saving computation on easier ones, and response reuse, which leverages previously generated correct responses to provide useful training signals. We compare AR3PO with strong RLVR baselines on multiple representative benchmarks using two different families of base models. Across the 7B and 8B models, AR3PO consistently outperforms GRPO and matches or surpasses DAPO (Yu et al., 2025), reducing rollout cost by up to 4.2x. On the larger 32B model, AR3PO achieves comparable performance to DAPO at similar training steps while maintaining substantially lower rollout cost.

Multimodal Large Language Models (MLLMs) have gained significant traction for their ability to process diverse input data types and generate coherent, contextually relevant outputs across various applications. While supervised fine-tuning (SFT) has been the predominant approach to enhance MLLM capabilities in task-specific optimization, it often falls short in fostering crucial generalized reasoning abilities. Although reinforcement learning (RL) holds great promise in overcoming these limitations, it encounters two significant challenges: (1) its generalized capacities in multimodal tasks remain largely unexplored, and (2) its training constraints, including the constant Kullback-Leibler divergence or the clamp strategy, often result in suboptimal bottlenecks. To address these challenges, we propose OThink-MR1, an advanced MLLM equipped with profound comprehension and reasoning capabilities across multimodal tasks. Specifically, we introduce Group Relative Policy Optimization with a dynamic Kullback-Leibler strategy (GRPO-D), which markedly enhances reinforcement learning (RL) performance. For Qwen2-VL-2B-Instruct, GRPO-D achieves a relative improvement of more than 5.72% over SFT and more than 13.59% over GRPO in same-task evaluation on two adapted datasets. Furthermore, GRPO-D demonstrates remarkable cross-task generalization capabilities, with an average relative improvement of more than 61.63% over SFT in cross-task evaluation. These results highlight that the MLLM trained with GRPO-D on one multimodal task can be effectively transferred to another task, underscoring the superior generalized reasoning capabilities of our proposed OThink-MR1 model.

As autonomous agents become adept at understanding and interacting with graphical user interface (GUI) environments, a new era of automated task execution is emerging. Recent studies have demonstrated that Reinforcement Learning (RL) can effectively enhance agents' performance in dynamic interactive GUI environments. However, these methods face two key limitations: (1) they overlook the significant variation in difficulty across different GUI tasks by treating the entire training data as a uniform set, which hampers the agent's ability to adapt its learning process; and (2) most approaches collapse task-specific nuances into a single, coarse reward, leaving the agent with a uniform signal that yields inefficient policy updates. To address these limitations, we propose CRAFT-GUI, a curriculum learning framework based on Group Relative Policy Optimization (GRPO) that explicitly accounts for the varying difficulty across trajectories. To enable more fine-grained policy optimization, we design a reward function that combines simple rule-based signals with model-judged evaluation, providing richer and more nuanced feedback during training. Experimental results demonstrate that our method achieves significant improvements over previous state-of-the-art approaches, outperforming them by 5.6% on public benchmarks Android Control and 10.3% on our internal online benchmarks, respectively. These findings empirically validate the effectiveness of integrating reinforcement learning with curriculum learning in GUI interaction tasks.

Mathematical reasoning poses a significant challenge for language models due to its complex and structured nature. In this paper, we introduce DeepSeekMath 7B, which continues pre-training DeepSeek-Coder-Base-v1.5 7B with 120B math-related tokens sourced from Common Crawl, together with natural language and code data. DeepSeekMath 7B has achieved an impressive score of 51.7% on the competition-level MATH benchmark without relying on external toolkits and voting techniques, approaching the performance level of Gemini-Ultra and GPT-4. Self-consistency over 64 samples from DeepSeekMath 7B achieves 60.9% on MATH. The mathematical reasoning capability of DeepSeekMath is attributed to two key factors: First, we harness the significant potential of publicly available web data through a meticulously engineered data selection pipeline. Second, we introduce Group Relative Policy Optimization (GRPO), a variant of Proximal Policy Optimization (PPO), that enhances mathematical reasoning abilities while concurrently optimizing the memory usage of PPO.

Recent advances of reasoning models, exemplified by OpenAI's o1 and DeepSeek's R1, highlight the significant potential of Reinforcement Learning (RL) to enhance the reasoning capabilities of Large Language Models (LLMs). However, replicating these advancements across diverse domains remains challenging due to limited methodological transparency. In this work, we present two-Staged history-Resampling Policy Optimization (SRPO), which successfully surpasses the performance of DeepSeek-R1-Zero-32B on the AIME24 and LiveCodeBench benchmarks. SRPO achieves this using the same base model as DeepSeek (i.e. Qwen2.5-32B) and relies solely on RL, without prior Supervised Fine-Tuning (SFT). Building upon Group Relative Policy Optimization (GRPO), we introduce two key methodological innovations: (1) a two-stage cross-domain training paradigm designed to balance the development of mathematical reasoning and coding proficiency, and (2) History Resampling (HR), a technique to address ineffective samples. Our comprehensive experiments validate the effectiveness of our approach, dedicating to offer valuable insights into scaling LLM reasoning capabilities across diverse tasks.

Reinforcement learning (RL) has emerged as an effective approach for enhancing the reasoning capabilities of large language models (LLMs), especially in scenarios where supervised fine-tuning (SFT) falls short due to limited chain-of-thought (CoT) data. Among RL-based post-training methods, group relative advantage estimation, as exemplified by Group Relative Policy Optimization (GRPO), has attracted considerable attention for eliminating the dependency on the value model, thereby simplifying training compared to traditional approaches like Proximal Policy Optimization (PPO). However, we observe that exsiting group relative advantage estimation method still suffers from training inefficiencies, particularly when the estimated advantage approaches zero. To address this limitation, we propose Advantage-Augmented Policy Optimization (AAPO), a novel RL algorithm that optimizes the cross-entropy (CE) loss using advantages enhanced through a momentum-based estimation scheme. This approach effectively mitigates the inefficiencies associated with group relative advantage estimation. Experimental results on multiple mathematical reasoning benchmarks demonstrate the superior performance of AAPO.

Reinforcement learning often needs to deal with the exponential growth of states and actions when exploring optimal control in high-dimensional spaces (often known as the curse of dimensionality). In this work, we address this issue by learning the inherent structure of action-wise similar MDP to appropriately balance the performance degradation versus sample/computational complexity. In particular, we partition the action spaces into multiple groups based on the similarity in transition distribution and reward function, and build a linear decomposition model to capture the difference between the intra-group transition kernel and the intra-group rewards. Both our theoretical analysis and experiments reveal a surprising and counter-intuitive result: while a more refined grouping strategy can reduce the approximation error caused by treating actions in the same group as identical, it also leads to increased estimation error when the size of samples or the computation resources is limited. This finding highlights the grouping strategy as a new degree of freedom that can be optimized to minimize the overall performance loss. To address this issue, we formulate a general optimization problem for determining the optimal grouping strategy, which strikes a balance between performance loss and sample/computational complexity. We further propose a computationally efficient method for selecting a nearly-optimal grouping strategy, which maintains its computational complexity independent of the size of the action space.

This paper provides a self-contained, from-scratch, exposition of key algorithms for instruction tuning of models: SFT, Rejection Sampling, REINFORCE, Trust Region Policy Optimization (TRPO), Proximal Policy Optimization (PPO), Group Relative Policy Optimization (GRPO), and Direct Preference Optimization (DPO). Explanations of these algorithms often assume prior knowledge, lack critical details, and/or are overly generalized and complex. Here, each method is discussed and developed step by step using simplified and explicit notation focused on LLMs, aiming to eliminate ambiguity and provide a clear and intuitive understanding of the concepts. By minimizing detours into the broader RL literature and connecting concepts to LLMs, we eliminate superfluous abstractions and reduce cognitive overhead. Following this exposition, we provide a literature review of new techniques and approaches beyond those detailed. Finally, new ideas for research and exploration in the form of GRAPE (Generalized Relative Advantage Policy Evolution) are presented.

We introduce VisTA, a new reinforcement learning framework that empowers visual agents to dynamically explore, select, and combine tools from a diverse library based on empirical performance. Existing methods for tool-augmented reasoning either rely on training-free prompting or large-scale fine-tuning; both lack active tool exploration and typically assume limited tool diversity, and fine-tuning methods additionally demand extensive human supervision. In contrast, VisTA leverages end-to-end reinforcement learning to iteratively refine sophisticated, query-specific tool selection strategies, using task outcomes as feedback signals. Through Group Relative Policy Optimization (GRPO), our framework enables an agent to autonomously discover effective tool-selection pathways without requiring explicit reasoning supervision. Experiments on the ChartQA, Geometry3K, and BlindTest benchmarks demonstrate that VisTA achieves substantial performance gains over training-free baselines, especially on out-of-distribution examples. These results highlight VisTA's ability to enhance generalization, adaptively utilize diverse tools, and pave the way for flexible, experience-driven visual reasoning systems.

Reinforcement Learning (RL) can directly enhance the reasoning capabilities of large language models without extensive reliance on Supervised Fine-Tuning (SFT). In this work, we revisit the traditional Policy Gradient (PG) mechanism and propose a minimalist RL approach termed Group Policy Gradient (GPG). Unlike conventional methods, GPG directly optimize the original RL objective, thus obviating the need for surrogate loss functions. As illustrated in our paper, by eliminating both the critic and reference models, and avoiding KL divergence constraints, our approach significantly simplifies the training process when compared to Group Relative Policy Optimization (GRPO). Our approach achieves superior performance without relying on auxiliary techniques or adjustments. Extensive experiments demonstrate that our method not only reduces computational costs but also consistently outperforms GRPO across various unimodal and multimodal tasks. Our code is available at https://github.com/AMAP-ML/GPG.

This paper introduces Multi-Agent MDP Homomorphic Networks, a class of networks that allows distributed execution using only local information, yet is able to share experience between global symmetries in the joint state-action space of cooperative multi-agent systems. In cooperative multi-agent systems, complex symmetries arise between different configurations of the agents and their local observations. For example, consider a group of agents navigating: rotating the state globally results in a permutation of the optimal joint policy. Existing work on symmetries in single agent reinforcement learning can only be generalized to the fully centralized setting, because such approaches rely on the global symmetry in the full state-action spaces, and these can result in correspondences across agents. To encode such symmetries while still allowing distributed execution we propose a factorization that decomposes global symmetries into local transformations. Our proposed factorization allows for distributing the computation that enforces global symmetries over local agents and local interactions. We introduce a multi-agent equivariant policy network based on this factorization. We show empirically on symmetric multi-agent problems that globally symmetric distributable policies improve data efficiency compared to non-equivariant baselines.

Recent advances in reinforcement learning for foundation models, such as Group Relative Policy Optimization (GRPO), have significantly improved the performance of foundation models on reasoning tasks. Notably, the advantage function serves as a central mechanism in GRPO for ranking the trajectory importance. However, existing explorations encounter both advantage reversion and advantage mirror problems, which hinder the reasonable advantage allocation across different query samples. In this work, we propose an easy but effective GRPO strategy, Mixed Advantage Policy Optimization (MAPO). We reveal that the trajectory appears with different certainty and propose the advantage percent deviation for samples with high-certainty trajectories. Furthermore, we dynamically reweight the advantage function for samples with varying trajectory certainty, thereby adaptively configuring the advantage function to account for sample-specific characteristics. Comparison with related state-of-the-art methods, along with ablation studies on different advantage variants, validates the effectiveness of our approach.

Policy-based optimizations are widely adopted today for the training and alignment of language models, where one of the most recent and effective approaches is Group-relative Policy Optimization (GRPO). In this paper, we reveals and analyze two major limitations of GRPO: (i) tokens frequently appear in completions with both positive and negative rewards, leading to conflicting gradient updates that can reduce their output probability, even though can be essential for maintaining proper structure; (ii) negatively rewarded completions may penalize confident responses and shift model decisions toward unlikely tokens, progressively flattening the output distribution and degrading learning. To address these issues and provide a more stable and effective policy optimization strategy, we introduce GTPO (Group-relative Trajectory-based Policy Optimization), which identifies conflict tokens, tokens appearing in the same position across completions with opposite rewards, protects them by skipping negative updates, while amplifying positive ones. To further prevent policy collapse, GTPO filters out completions whose entropy exceeds a provable threshold. Unlike GRPO, GTPO does not rely on KL-divergence regularization, eliminating the need for a reference model during training, while still ensuring greater training stability and improved performance, validated through multiple experiments on GSM8K, MATH and AIME 2024 benchmarks.

Recent advances in Large Language Model (LLM) agents have demonstrated their promising general capabilities. However, their performance in specialized real-world domains often degrades due to challenges in effectively integrating external tools and specific prompting strategies. While methods like agentic reinforcement learning have been proposed to address this, they typically rely on costly parameter updates, for example, through a process that uses Supervised Fine-Tuning (SFT) followed by a Reinforcement Learning (RL) phase with Group Relative Policy Optimization (GRPO) to alter the output distribution. However, we argue that LLMs can achieve a similar effect on the output distribution by learning experiential knowledge as a token prior, which is a far more lightweight approach that not only addresses practical data scarcity but also avoids the common issue of overfitting. To this end, we propose Training-Free Group Relative Policy Optimization (Training-Free GRPO), a cost-effective solution that enhances LLM agent performance without any parameter updates. Our method leverages the group relative semantic advantage instead of numerical ones within each group of rollouts, iteratively distilling high-quality experiential knowledge during multi-epoch learning on a minimal ground-truth data. Such knowledge serves as the learned token prior, which is seamlessly integrated during LLM API calls to guide model behavior. Experiments on mathematical reasoning and web searching tasks demonstrate that Training-Free GRPO, when applied to DeepSeek-V3.1-Terminus, significantly improves out-of-domain performance. With just a few dozen training samples, Training-Free GRPO outperforms fine-tuned small LLMs with marginal training data and cost.

Large language models have demonstrated strong reasoning capabilities in complex tasks through tool integration, which is typically framed as a Markov Decision Process and optimized with trajectory-level RL algorithms such as GRPO. However, a common class of reasoning tasks, iterative optimization, presents distinct challenges: the agent interacts with the same underlying environment state across turns, and the value of a trajectory is determined by the best turn-level reward rather than cumulative returns. Existing GRPO-based methods cannot perform fine-grained, turn-level optimization in such settings, while black-box optimization methods discard prior knowledge and reasoning capabilities. To address this gap, we propose Turn-Level GRPO (TL-GRPO), a lightweight RL algorithm that performs turn-level group sampling for fine-grained optimization. We evaluate TL-GRPO on analog circuit sizing (ACS), a challenging scientific optimization task requiring multiple simulations and domain expertise. Results show that TL-GRPO outperforms standard GRPO and Bayesian optimization methods across various specifications. Furthermore, our 30B model trained with TL-GRPO achieves state-of-the-art performance on ACS tasks under same simulation budget, demonstrating both strong generalization and practical utility.

Large language model (LLM)-based agents are increasingly trained with reinforcement learning (RL) to enhance their ability to interact with external environments through tool use, particularly in search-based settings that require multi-turn reasoning and knowledge acquisition. However, existing approaches typically rely on outcome-based rewards that are only provided at the final answer. This reward sparsity becomes particularly problematic in multi-turn settings, where long trajectories exacerbate two critical issues: (i) advantage collapse, where all rollouts receive identical rewards and provide no useful learning signals, and (ii) lack of fine-grained credit assignment, where dependencies between turns are obscured, especially in long-horizon tasks. In this paper, we propose Information Gain-based Policy Optimization (IGPO), a simple yet effective RL framework that provides dense and intrinsic supervision for multi-turn agent training. IGPO models each interaction turn as an incremental process of acquiring information about the ground truth, and defines turn-level rewards as the marginal increase in the policy's probability of producing the correct answer. Unlike prior process-level reward approaches that depend on external reward models or costly Monte Carlo estimation, IGPO derives intrinsic rewards directly from the model's own belief updates. These intrinsic turn-level rewards are combined with outcome-level supervision to form dense reward trajectories. Extensive experiments on both in-domain and out-of-domain benchmarks demonstrate that IGPO consistently outperforms strong baselines in multi-turn scenarios, achieving higher accuracy and improved sample efficiency.

Multimodal reasoning over long-horizon video is challenging due to the need for precise spatiotemporal fusion and alignment across modalities. While recent methods such as Group Relative Policy Optimization (GRPO) have shown promise in this domain, they suffer from three key limitations: (1) data inefficiency from their on-policy design, (2) a vanishing advantage problem, where identical or near-identical rewards within a group eliminate the learning signal by producing zero-valued advantages, and (3) uniform credit assignment that fails to emphasize critical reasoning steps. We introduce AVATAR (Audio-Video Agent for Alignment and Reasoning), a framework that addresses these limitations through two core components: (1) an off-policy training architecture that improves sample efficiency and resolves vanishing advantages by reusing past experiences with greater reward diversity, and (2) Temporal Advantage Shaping (TAS), a novel credit assignment strategy that upweights key reasoning phases during learning. AVATAR achieves strong performance across various benchmarks, outperforming the Qwen2.5-Omni baseline by +5.4on MMVU, +4.9 on OmniBench, and +4.5 on Video-Holmes, while demonstrating over 35% higher sample efficiency.

Off-policy reinforcement learning (RL) for large language models (LLMs) is attracting growing interest, driven by practical constraints in real-world applications, the complexity of LLM-RL infrastructure, and the need for further innovations of RL methodologies. While classic REINFORCE and its modern variants like Group Relative Policy Optimization (GRPO) are typically regarded as on-policy algorithms with limited tolerance of off-policyness, we present in this work a first-principles derivation for group-relative REINFORCE without assuming a specific training data distribution, showing that it admits a native off-policy interpretation. This perspective yields two general principles for adapting REINFORCE to off-policy settings: regularizing policy updates, and actively shaping the data distribution. Our analysis demystifies some myths about the roles of importance sampling and clipping in GRPO, unifies and reinterprets two recent algorithms -- Online Policy Mirror Descent (OPMD) and Asymmetric REINFORCE (AsymRE) -- as regularized forms of the REINFORCE loss, and offers theoretical justification for seemingly heuristic data-weighting strategies. Our findings lead to actionable insights that are validated with extensive empirical studies, and open up new opportunities for principled algorithm design in off-policy RL for LLMs. Source code for this work is available at https://github.com/modelscope/Trinity-RFT/tree/main/examples/rec_gsm8k.

The recent success and openness of DeepSeek-R1 have brought widespread attention to Group Relative Policy Optimization (GRPO) as a reinforcement learning method for large reasoning models (LRMs). In this work, we analyze the GRPO objective under a binary reward setting and reveal an inherent limitation of question-level difficulty bias. We also identify a connection between GRPO and traditional discriminative methods in supervised learning. Motivated by these insights, we introduce a new Discriminative Constrained Optimization (DisCO) framework for reinforcing LRMs, grounded in the principle of discriminative learning. The main differences between DisCO and GRPO and its recent variants are: (1) it replaces the group relative objective with a discriminative objective defined by a scoring function; (2) it abandons clipping-based surrogates in favor of non-clipping RL surrogate objectives used as scoring functions; (3) it employs a simple yet effective constrained optimization approach to enforce the KL divergence constraint, ensuring stable training. As a result, DisCO offers notable advantages over GRPO and its variants: (i) it completely eliminates difficulty bias by adopting discriminative objectives; (ii) it addresses the entropy instability in GRPO and its variants through the use of non-clipping scoring functions and a constrained optimization approach; (iii) it allows the incorporation of advanced discriminative learning techniques to address data imbalance, where a significant number of questions have more negative than positive generated answers during training. Our experiments on enhancing the mathematical reasoning capabilities of SFT-finetuned models show that DisCO significantly outperforms GRPO and its improved variants such as DAPO, achieving average gains of 7\% over GRPO and 6\% over DAPO across six benchmark tasks for an 1.5B model.

Enhancing the reasoning capabilities of large language models (LLMs) typically relies on massive computational resources and extensive datasets, limiting accessibility for resource-constrained settings. Our study investigates the potential of reinforcement learning (RL) to improve reasoning in small LLMs, focusing on a 1.5-billion-parameter model, DeepSeek-R1-Distill-Qwen-1.5B, under strict constraints: training on 4 NVIDIA A40 GPUs (48 GB VRAM each) within 24 hours. Adapting the Group Relative Policy Optimization (GRPO) algorithm and curating a compact, high-quality mathematical reasoning dataset, we conducted three experiments to explore model behavior and performance. Our results demonstrate rapid reasoning gains - e.g., AMC23 accuracy rising from 63% to 80% and AIME24 reaching 46.7%, surpassing o1-preview - using only 7,000 samples and a $42 training cost, compared to thousands of dollars for baseline models. However, challenges such as optimization instability and length constraints emerged with prolonged training. These findings highlight the efficacy of RL-based fine-tuning for small LLMs, offering a cost-effective alternative to large-scale approaches. We release our code and datasets as open-source resources, providing insights into trade-offs and laying a foundation for scalable, reasoning-capable LLMs in resource-limited environments. All are available at https://github.com/knoveleng/open-rs.

We present Seg-R1, a preliminary exploration of using reinforcement learning (RL) to enhance the pixel-level understanding and reasoning capabilities of large multimodal models (LMMs). Starting with foreground segmentation tasks, specifically camouflaged object detection (COD) and salient object detection (SOD), our approach enables the LMM to generate point and bounding box prompts in the next-token fashion, which are then used to guide SAM2 in producing segmentation masks. We introduce Group Relative Policy Optimization (GRPO) into the segmentation domain, equipping the LMM with pixel-level comprehension through a carefully designed training strategy. Notably, Seg-R1 achieves remarkable performance with purely RL-based training, achieving .873 S-measure on COD10K without complex model modification. Moreover, we found that pure RL training demonstrates strong open-world generalization. Despite being trained solely on foreground segmentation image-mask pairs without text supervision, Seg-R1 achieves impressive zero-shot performance on referring segmentation and reasoning segmentation tasks, with 71.4 cIoU on RefCOCOg test and 56.7 gIoU on ReasonSeg test, outperforming models fully supervised on these datasets.

While reinforcement learning methods such as Group Relative Preference Optimization (GRPO) have significantly enhanced Large Language Models, adapting them to diffusion models remains challenging. In particular, GRPO demands a stochastic policy, yet the most cost-effective diffusion samplers are based on deterministic ODEs. Recent work addresses this issue by using inefficient SDE-based samplers to induce stochasticity, but this reliance on model-agnostic Gaussian noise leads to slow convergence. To resolve this conflict, we propose Direct Group Preference Optimization (DGPO), a new online RL algorithm that dispenses with the policy-gradient framework entirely. DGPO learns directly from group-level preferences, which utilize relative information of samples within groups. This design eliminates the need for inefficient stochastic policies, unlocking the use of efficient deterministic ODE samplers and faster training. Extensive results show that DGPO trains around 20 times faster than existing state-of-the-art methods and achieves superior performance on both in-domain and out-of-domain reward metrics. Code is available at https://github.com/Luo-Yihong/DGPO.

Recent advancements, such as Group Relative Policy Optimization (GRPO), have enhanced the reasoning capabilities of large language models by optimizing the arithmetic mean of token-level rewards. However, GRPO suffers from unstable policy updates when processing tokens with outlier importance-weighted rewards, which manifests as extreme importance sampling ratios during training, i.e., the ratio between the sampling probabilities assigned to a token by the current and old policies. In this work, we propose Geometric-Mean Policy Optimization (GMPO), a stabilized variant of GRPO. Instead of optimizing the arithmetic mean, GMPO maximizes the geometric mean of token-level rewards, which is inherently less sensitive to outliers and maintains a more stable range of importance sampling ratio. In addition, we provide comprehensive theoretical and experimental analysis to justify the design and stability benefits of GMPO. Beyond improved stability, GMPO-7B outperforms GRPO by an average of 4.1% on multiple mathematical benchmarks and 1.4% on multimodal reasoning benchmark, including AIME24, AMC, MATH500, OlympiadBench, Minerva, and Geometry3K. Code is available at https://github.com/callsys/GMPO.

Large reasoning models (LRM) with long chain-of-thought (CoT) capabilities have shown strong performance on objective tasks, such as math reasoning and coding. However, their effectiveness on subjective questions that may have different responses from different perspectives is still limited by a tendency towards homogeneous reasoning, introduced by the reliance on a single ground truth in supervised fine-tuning and verifiable reward in reinforcement learning. Motivated by the finding that increasing role perspectives consistently improves performance, we propose MultiRole-R1, a diversity-enhanced framework with multiple role perspectives, to improve the accuracy and diversity in subjective reasoning tasks. MultiRole-R1 features an unsupervised data construction pipeline that generates reasoning chains that incorporate diverse role perspectives. We further employ reinforcement learning via Group Relative Policy Optimization (GRPO) with reward shaping, by taking diversity as a reward signal in addition to the verifiable reward. With specially designed reward functions, we successfully promote perspective diversity and lexical diversity, uncovering a positive relation between reasoning diversity and accuracy. Our experiment on six benchmarks demonstrates MultiRole-R1's effectiveness and generalizability in enhancing both subjective and objective reasoning, showcasing the potential of diversity-enhanced training in LRMs.

Group-based policy optimization methods like GRPO and GSPO have become standard for training multimodal models, leveraging group-wise rollouts and relative advantage estimation. However, they suffer from a critical gradient vanishing problem when all responses within a group receive identical rewards, causing advantage estimates to collapse and training signals to diminish. Existing attempts to mitigate this issue fall into two paradigms: filtering-based and sampling-based methods. Filtering-based methods first generate rollouts broadly and then retroactively filter out uninformative groups, leading to substantial computational overhead. Sampling-based methods proactively select effective samples before rollout but rely on static criteria or prior dataset knowledge, lacking real-time adaptability. To address these issues, we propose VADE, a Variance-Aware Dynamic sampling framework via online sample-level difficulty Estimation. Our framework integrates three key components: online sample-level difficulty estimation using Beta distributions, a Thompson sampler that maximizes information gain through the estimated correctness probability, and a two-scale prior decay mechanism that maintains robust estimation under policy evolution. This three components design enables VADE to dynamically select the most informative samples, thereby amplifying training signals while eliminating extra rollout costs. Extensive experiments on multimodal reasoning benchmarks show that VADE consistently outperforms strong baselines in both performance and sample efficiency, while achieving a dramatic reduction in computational overhead. More importantly, our framework can serves as a plug-and-play component to be seamlessly integrated into existing group-based RL algorithms. Code and models are available at https://VADE-RL.github.io.

Social agents powered by large language models (LLMs) can simulate human social behaviors but fall short in handling complex goal-oriented social dialogues. Direct Preference Optimization (DPO) has proven effective in aligning LLM behavior with human preferences across a variety of agent tasks. Existing DPO-based approaches for multi-turn interactions are divided into turn-level and session-level methods. The turn-level method is overly fine-grained, focusing exclusively on individual turns, while session-level methods are too coarse-grained, often introducing training noise. To address these limitations, we propose Segment-Level Direct Preference Optimization (SDPO), which focuses on specific key segments within interactions to optimize multi-turn agent behavior while minimizing training noise. Evaluations on the SOTOPIA benchmark demonstrate that SDPO-tuned agents consistently outperform both existing DPO-based methods and proprietary LLMs like GPT-4o, underscoring SDPO's potential to advance the social intelligence of LLM-based agents. We release our code and data at https://github.com/AlibabaResearch/DAMO-ConvAI/tree/main/SDPO.

Graph Retrieval-Augmented Generation (GraphRAG) has shown great effectiveness in enhancing the reasoning abilities of LLMs by leveraging graph structures for knowledge representation and modeling complex real-world relationships. However, existing GraphRAG methods still face significant bottlenecks when handling complex problems that require multi-hop reasoning, as their query and retrieval phases are largely based on pre-defined heuristics and do not fully utilize the reasoning potentials of LLMs. To address this problem, we propose GraphRAG-R1, an adaptive GraphRAG framework by training LLMs with process-constrained outcome-based reinforcement learning (RL) to enhance the multi-hop reasoning ability. Our method can decompose complex problems, autonomously invoke retrieval tools to acquire necessary information, and perform effective reasoning. Specifically, we utilize a modified version of Group Relative Policy Optimization (GRPO) that supports rollout-with-thinking capability. Next, we design two process-constrained reward functions. To handle the shallow retrieval problem, we design a Progressive Retrieval Attenuation (PRA) reward to encourage essential retrievals. Then, to handle the over-thinking problem, we design Cost-Aware F1 (CAF) reward to balance the model performance with computational costs. We further design a phase-dependent training strategy, containing three training stages corresponding to cold start and these two rewards. Lastly, our method adopts a hybrid graph-textual retrieval to improve the reasoning capacity. Extensive experimental results demonstrate that GraphRAG-R1 boosts LLM capabilities in solving complex reasoning problems compared to state-of-the-art GraphRAG methods on both in-domain and out-of-domain datasets. Furthermore, our framework can be flexibly integrated with various existing retrieval methods, consistently delivering performance improvements.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as an effective approach for improving the reasoning abilities of large language models (LLMs). The Group Relative Policy Optimization (GRPO) family has demonstrated strong performance in training LLMs with RLVR. However, as models train longer and scale larger, more training prompts become residual prompts, those with zero variance rewards that provide no training signal. Consequently, fewer prompts contribute to training, reducing diversity and hindering effectiveness. To fully exploit these residual prompts, we propose the Explore Residual Prompts in Policy Optimization (ERPO) framework, which encourages exploration on residual prompts and reactivates their training signals. ERPO maintains a history tracker for each prompt and adaptively increases the sampling temperature for residual prompts that previously produced all correct responses. This encourages the model to generate more diverse reasoning traces, introducing incorrect responses that revive training signals. Empirical results on the Qwen2.5 series demonstrate that ERPO consistently surpasses strong baselines across multiple mathematical reasoning benchmarks.

Recent advancements in reinforcement learning, particularly through Group Relative Policy Optimization (GRPO), have significantly improved multimodal large language models for complex reasoning tasks. However, two critical limitations persist: 1) they often produce unfocused, verbose reasoning chains that obscure salient spatiotemporal cues and 2) binary rewarding fails to account for partially correct answers, resulting in high reward variance and inefficient learning. In this paper, we propose TW-GRPO, a novel framework that enhances visual reasoning with focused thinking and dense reward granularity. Specifically, we employs a token weighting mechanism that prioritizes tokens with high informational density (estimated by intra-group variance), suppressing redundant tokens like generic reasoning prefixes. Furthermore, we reformulate RL training by shifting from single-choice to multi-choice QA tasks, where soft rewards enable finer-grained gradient estimation by distinguishing partial correctness. Additionally, we propose question-answer inversion, a data augmentation strategy to generate diverse multi-choice samples from existing benchmarks. Experiments demonstrate state-of-the-art performance on several video reasoning and general understanding benchmarks. Notably, TW-GRPO achieves 50.4\% accuracy on CLEVRER (18.8\% improvement over Video-R1) and 65.8\% on MMVU. Our codes are available at https://github.com/longmalongma/TW-GRPO.

Post-training plays a crucial role in refining and aligning large language models to meet specific tasks and human preferences. While recent advancements in post-training techniques, such as Group Relative Policy Optimization (GRPO), leverage increased sampling with relative reward scoring to achieve superior performance, these methods often suffer from training instability that limits their practical adoption. To address this challenge, we present Group Variance Policy Optimization (GVPO). GVPO incorporates the analytical solution to KL-constrained reward maximization directly into its gradient weights, ensuring alignment with the optimal policy. The method provides intuitive physical interpretations: its gradient mirrors the mean squared error between the central distance of implicit rewards and that of actual rewards. GVPO offers two key advantages: (1) it guarantees a unique optimal solution, exactly the KL-constrained reward maximization objective, (2) it supports flexible sampling distributions that avoids on-policy and importance sampling limitations. By unifying theoretical guarantees with practical adaptability, GVPO establishes a new paradigm for reliable and versatile LLM post-training.

Diffusion Language Models (dLLMs) have emerged as promising alternatives to Auto-Regressive (AR) models. While recent efforts have validated their pre-training potential and accelerated inference speeds, the post-training landscape for dLLMs remains underdeveloped. Existing methods suffer from computational inefficiency and objective mismatches between training and inference, severely limiting performance on complex reasoning tasks such as mathematics. To address this, we introduce DiRL, an efficient post-training framework that tightly integrates FlexAttention-accelerated blockwise training with LMDeploy-optimized inference. This architecture enables a streamlined online model update loop, facilitating efficient two-stage post-training (Supervised Fine-Tuning followed by Reinforcement Learning). Building on this framework, we propose DiPO, the first unbiased Group Relative Policy Optimization (GRPO) implementation tailored for dLLMs. We validate our approach by training DiRL-8B-Instruct on high-quality math data. Our model achieves state-of-the-art math performance among dLLMs and surpasses comparable models in the Qwen2.5 series on several benchmarks.

Multimodal Retrieval-Augmented Generation (MRAG) has shown promise in mitigating hallucinations in Multimodal Large Language Models (MLLMs) by incorporating external knowledge during generation. Existing MRAG methods typically adopt a static retrieval pipeline that fetches relevant information from multiple Knowledge Bases (KBs), followed by a refinement step. However, these approaches overlook the reasoning and planning capabilities of MLLMs to dynamically determine how to interact with different KBs during the reasoning process. To address this limitation, we propose R1-Router, a novel MRAG framework that learns to decide when and where to retrieve knowledge based on the evolving reasoning state. Specifically, R1-Router can generate follow-up queries according to the current reasoning step, routing these intermediate queries to the most suitable KB, and integrating external knowledge into a coherent reasoning trajectory to answer the original query. Furthermore, we introduce Step-wise Group Relative Policy Optimization (Step-GRPO), a tailored reinforcement learning algorithm that assigns step-specific rewards to optimize the reasoning behavior of MLLMs. Experimental results on various open-domain QA benchmarks across multiple modalities demonstrate that R1-Router outperforms baseline models by over 7%. Further analysis shows that R1-Router can adaptively and effectively leverage diverse KBs, reducing unnecessary retrievals and improving both efficiency and accuracy.

DeepSeek-R1-Zero has shown that reinforcement learning (RL) at scale can directly enhance the reasoning capabilities of LLMs without supervised fine-tuning. In this work, we critically examine R1-Zero-like training by analyzing its two core components: base models and RL. We investigate a wide range of base models, including DeepSeek-V3-Base, to understand how pretraining characteristics influence RL performance. Our analysis reveals that DeepSeek-V3-Base already exhibit ''Aha moment'', while Qwen2.5 base models demonstrate strong reasoning capabilities even without prompt templates, suggesting potential pretraining biases. Additionally, we identify an optimization bias in Group Relative Policy Optimization (GRPO), which artificially increases response length (especially for incorrect outputs) during training. To address this, we introduce Dr. GRPO, an unbiased optimization method that improves token efficiency while maintaining reasoning performance. Leveraging these insights, we present a minimalist R1-Zero recipe that achieves 43.3% accuracy on AIME 2024 with a 7B base model, establishing a new state-of-the-art. Our code is available at https://github.com/sail-sg/understand-r1-zero.

Latent World Models enhance scene representation through temporal self-supervised learning, presenting a perception annotation-free paradigm for end-to-end autonomous driving. However, the reconstruction-oriented representation learning tangles perception with planning tasks, leading to suboptimal optimization for planning. To address this challenge, we propose WorldRFT, a planning-oriented latent world model framework that aligns scene representation learning with planning via a hierarchical planning decomposition and local-aware interactive refinement mechanism, augmented by reinforcement learning fine-tuning (RFT) to enhance safety-critical policy performance. Specifically, WorldRFT integrates a vision-geometry foundation model to improve 3D spatial awareness, employs hierarchical planning task decomposition to guide representation optimization, and utilizes local-aware iterative refinement to derive a planning-oriented driving policy. Furthermore, we introduce Group Relative Policy Optimization (GRPO), which applies trajectory Gaussianization and collision-aware rewards to fine-tune the driving policy, yielding systematic improvements in safety. WorldRFT achieves state-of-the-art (SOTA) performance on both open-loop nuScenes and closed-loop NavSim benchmarks. On nuScenes, it reduces collision rates by 83% (0.30% -> 0.05%). On NavSim, using camera-only sensors input, it attains competitive performance with the LiDAR-based SOTA method DiffusionDrive (87.8 vs. 88.1 PDMS).

Reinforcement learning from verifiable rewards has emerged as a powerful technique for enhancing the complex reasoning abilities of Large Language Models (LLMs). However, these methods are fundamentally constrained by the ''learning cliff'' phenomenon: when faced with problems far beyond their current capabilities, models consistently fail, yielding a persistent zero-reward signal. In policy optimization algorithms like GRPO, this collapses the advantage calculation to zero, rendering these difficult problems invisible to the learning gradient and stalling progress. To overcome this, we introduce Scaf-GRPO (Scaffolded Group Relative Policy Optimization), a progressive training framework that strategically provides minimal guidance only when a model's independent learning has plateaued. The framework first diagnoses learning stagnation and then intervenes by injecting tiered in-prompt hints, ranging from abstract concepts to concrete steps, enabling the model to construct a valid solution by itself. Extensive experiments on challenging mathematics benchmarks demonstrate Scaf-GRPO's effectiveness, boosting the pass@1 score of the Qwen2.5-Math-7B model on the AIME24 benchmark by a relative 44.3% over a vanilla GRPO baseline. This result demonstrates our framework provides a robust and effective methodology for unlocking a model's ability to solve problems previously beyond its reach, a critical step towards extending the frontier of autonomous reasoning in LLM.

This paper explores multi-scenario optimization on large platforms using multi-agent reinforcement learning (MARL). We address this by treating scenarios like search, recommendation, and advertising as a cooperative, partially observable multi-agent decision problem. We introduce the Multi-Agent Recurrent Deterministic Policy Gradient (MARDPG) algorithm, which aligns different scenarios under a shared objective and allows for strategy communication to boost overall performance. Our results show marked improvements in metrics such as click-through rate (CTR), conversion rate, and total sales, confirming our method's efficacy in practical settings.

Tool-integrated reasoning (TIR) augments large language models (LLMs) with the ability to invoke external tools, such as search engines and code interpreters, to solve tasks beyond the capabilities of language-only reasoning. While reinforcement learning (RL) has shown promise in improving TIR by optimizing final answer correctness, existing approaches often overlook the efficiency and cost associated with tool usage. This can lead to suboptimal behavior, including excessive tool calls that increase computational and financial overhead, or insufficient tool use that compromises answer quality. In this work, we propose Optimal Tool Call-controlled Policy Optimization (OTC-PO), a simple yet effective RL-based framework that encourages models to produce accurate answers with minimal tool calls. Our method introduces a tool-integrated reward that jointly considers correctness and tool efficiency, promoting high tool productivity. We instantiate this framework within both Proximal Policy Optimization (PPO) and Group Relative Preference Optimization (GRPO), resulting in OTC-PPO and OTC-GRPO. Experiments with Qwen-2.5 and Qwen-Math across multiple QA benchmarks show that our approach reduces tool calls by up to 73.1\% and improves tool productivity by up to 229.4\%, while maintaining comparable answer accuracy. To the best of our knowledge, this is the first RL-based framework that explicitly optimizes tool-use efficiency in TIR.

Charts are essential to data analysis, transforming raw data into clear visual representations that support human decision-making. Although current vision-language models (VLMs) have made significant progress, they continue to struggle with chart comprehension due to training on datasets that lack diversity and real-world authenticity, or on automatically extracted underlying data tables of charts, which can contain numerous estimation errors. Furthermore, existing models only rely on supervised fine-tuning using these low-quality datasets, severely limiting their effectiveness. To address these issues, we first propose BigCharts, a dataset creation pipeline that generates visually diverse chart images by conditioning the rendering process on real-world charts sourced from multiple online platforms. Unlike purely synthetic datasets, BigCharts incorporates real-world data, ensuring authenticity and visual diversity, while still retaining accurate underlying data due to our proposed replotting process. Additionally, we introduce a comprehensive training framework that integrates supervised fine-tuning with Group Relative Policy Optimization (GRPO)-based reinforcement learning. By introducing novel reward signals specifically designed for chart reasoning, our approach enhances model robustness and generalization across diverse chart styles and domains, resulting in a state-of-the-art chart reasoning model, BigCharts-R1. Extensive experiments demonstrate that our models surpass existing methods on multiple chart question-answering benchmarks compared to even larger open-source and closed-source models.

Reinforcement learning (RL)-based post-training has been crucial for enabling multi-step reasoning in large reasoning models (LRMs), yet current reward schemes are typically outcome-centric. We propose PM4GRPO, a reasoning-aware Group Relative Policy Optimization (GRPO) that augments standard answer/format rewards with signals over the reasoning procedure. To this end, process mining techniques are utilized to compute a scalar conformance reward that measures how closely a policy model's reasoning aligns with the pretrained teacher model. The empirical results on five benchmarks demonstrate that PM4GRPO significantly outperforms existing methodologies for GRPO-based post-training. These results highlight that leveraging process mining for reasoning-aware GRPO effectively enhances the reasoning capabilities of policy models.

Large Language Models (LLMs) are increasingly deployed in business-critical domains such as finance, education, healthcare, and customer support, where users expect consistent and reliable recommendations. Yet LLMs often exhibit variability when prompts are phrased with minor differences, even when semantically equivalent. Such inconsistency undermines trust, complicates compliance, and disrupts user experience. While personalization is desirable in certain contexts, many enterprise scenarios-such as HR onboarding, customer support, or policy disclosure-require invariant information delivery regardless of phrasing or prior conversational history. Existing approaches, including retrieval-augmented generation (RAG) and temperature tuning, improve factuality or reduce stochasticity but cannot guarantee stability across equivalent prompts. In this paper, we propose a reinforcement learning framework based on Group Relative Policy Optimization (GRPO) to directly optimize for consistency. Unlike prior applications of GRPO, which have been limited to reasoning and code generation, we adapt GRPO to enforce stability of information content across groups of semantically equivalent prompts. We introduce entropy-based helpfulness and stability rewards, treating prompt variants as groups and resetting conversational context to isolate phrasing effects. Experiments on investment and job recommendation tasks show that our GRPO-trained model reduces variability more effectively than fine-tuning or decoding-based baselines. To our knowledge, this is a novel application of GRPO for aligning LLMs toward information consistency, reframing variability not as an acceptable feature of generative diversity but as a correctable flaw in enterprise deployments.

Recent reinforcement learning has enhanced the flow matching models on human preference alignment. While stochastic sampling enables the exploration of denoising directions, existing methods which optimize over multiple denoising steps suffer from sparse and ambiguous reward signals. We observe that the high entropy steps enable more efficient and effective exploration while the low entropy steps result in undistinguished roll-outs. To this end, we propose E-GRPO, an entropy aware Group Relative Policy Optimization to increase the entropy of SDE sampling steps. Since the integration of stochastic differential equations suffer from ambiguous reward signals due to stochasticity from multiple steps, we specifically merge consecutive low entropy steps to formulate one high entropy step for SDE sampling, while applying ODE sampling on other steps. Building upon this, we introduce multi-step group normalized advantage, which computes group-relative advantages within samples sharing the same consolidated SDE denoising step. Experimental results on different reward settings have demonstrated the effectiveness of our methods.

Large language models (LLMs) have demonstrated remarkable reasoning abilities in complex tasks, often relying on Chain-of-Thought (CoT) reasoning. However, due to their autoregressive token-level generation, the reasoning process is largely constrained to local decision-making and lacks global planning. This limitation frequently results in redundant, incoherent, or inaccurate reasoning, which significantly degrades overall performance. Existing approaches, such as tree-based algorithms and reinforcement learning (RL), attempt to address this issue but suffer from high computational costs and often fail to produce optimal reasoning trajectories. To tackle this challenge, we propose Plan-Then-Action Enhanced Reasoning with Group Relative Policy Optimization PTA-GRPO, a two-stage framework designed to improve both high-level planning and fine-grained CoT reasoning. In the first stage, we leverage advanced LLMs to distill CoT into compact high-level guidance, which is then used for supervised fine-tuning (SFT). In the second stage, we introduce a guidance-aware RL method that jointly optimizes the final output and the quality of high-level guidance, thereby enhancing reasoning effectiveness. We conduct extensive experiments on multiple mathematical reasoning benchmarks, including MATH, AIME2024, AIME2025, and AMC, across diverse base models such as Qwen2.5-7B-Instruct, Qwen3-8B, Qwen3-14B, and LLaMA3.2-3B. Experimental results demonstrate that PTA-GRPO consistently achieves stable and significant improvements across different models and tasks, validating its effectiveness and generalization.

Group Relative Policy Optimization (GRPO) has shown strong potential for flow-matching-based text-to-image (T2I) generation, but it faces two key limitations: inaccurate advantage attribution, and the neglect of temporal dynamics of generation. In this work, we argue that shifting the optimization paradigm from the step level to the chunk level can effectively alleviate these issues. Building on this idea, we propose Chunk-GRPO, the first chunk-level GRPO-based approach for T2I generation. The insight is to group consecutive steps into coherent 'chunk's that capture the intrinsic temporal dynamics of flow matching, and to optimize policies at the chunk level. In addition, we introduce an optional weighted sampling strategy to further enhance performance. Extensive experiments show that ChunkGRPO achieves superior results in both preference alignment and image quality, highlighting the promise of chunk-level optimization for GRPO-based methods.

Fine-tuning pre-trained generative models with Reinforcement Learning (RL) has emerged as an effective approach for aligning outputs more closely with nuanced human preferences. In this paper, we investigate the application of Group Relative Policy Optimization (GRPO) to fine-tune next-scale visual autoregressive (VAR) models. Our empirical results demonstrate that this approach enables alignment to intricate reward signals derived from aesthetic predictors and CLIP embeddings, significantly enhancing image quality and enabling precise control over the generation style. Interestingly, by leveraging CLIP, our method can help VAR models generalize beyond their initial ImageNet distribution: through RL-driven exploration, these models can generate images aligned with prompts referencing image styles that were absent during pre-training. In summary, we show that RL-based fine-tuning is both efficient and effective for VAR models, benefiting particularly from their fast inference speeds, which are advantageous for online sampling, an aspect that poses significant challenges for diffusion-based alternatives.

Recent advancements underscore the significant role of Reinforcement Learning (RL) in enhancing the Chain-of-Thought (CoT) reasoning capabilities of large language models (LLMs). Two prominent RL algorithms, Direct Preference Optimization (DPO) and Group Relative Policy Optimization (GRPO), are central to these developments, showcasing different pros and cons. Autoregressive image generation, also interpretable as a sequential CoT reasoning process, presents unique challenges distinct from LLM-based CoT reasoning. These encompass ensuring text-image consistency, improving image aesthetic quality, and designing sophisticated reward models, rather than relying on simpler rule-based rewards. While recent efforts have extended RL to this domain, these explorations typically lack an in-depth analysis of the domain-specific challenges and the characteristics of different RL strategies. To bridge this gap, we provide the first comprehensive investigation of the GRPO and DPO algorithms in autoregressive image generation, evaluating their in-domain performance and out-of-domain generalization, while scrutinizing the impact of different reward models on their respective capabilities. Our findings reveal that GRPO and DPO exhibit distinct advantages, and crucially, that reward models possessing stronger intrinsic generalization capabilities potentially enhance the generalization potential of the applied RL algorithms. Furthermore, we systematically explore three prevalent scaling strategies to enhance both their in-domain and out-of-domain proficiency, deriving unique insights into efficiently scaling performance for each paradigm. We hope our study paves a new path for inspiring future work on developing more effective RL algorithms to achieve robust CoT reasoning in the realm of autoregressive image generation. Code is released at https://github.com/ZiyuGuo99/Image-Generation-CoT

Multi-step learning applies lookahead over multiple time steps and has proved valuable in policy evaluation settings. However, in the optimal control case, the impact of multi-step learning has been relatively limited despite a number of prior efforts. Fundamentally, this might be because multi-step policy improvements require operations that cannot be approximated by stochastic samples, hence hindering the widespread adoption of such methods in practice. To address such limitations, we introduce doubly multi-step off-policy VI (DoMo-VI), a novel oracle algorithm that combines multi-step policy improvements and policy evaluations. DoMo-VI enjoys guaranteed convergence speed-up to the optimal policy and is applicable in general off-policy learning settings. We then propose doubly multi-step off-policy actor-critic (DoMo-AC), a practical instantiation of the DoMo-VI algorithm. DoMo-AC introduces a bias-variance trade-off that ensures improved policy gradient estimates. When combined with the IMPALA architecture, DoMo-AC has showed improvements over the baseline algorithm on Atari-57 game benchmarks.

We study the variance of stochastic policy gradients (SPGs) with many action samples per state. We derive a many-actions optimality condition, which determines when many-actions SPG yields lower variance as compared to a single-action agent with proportionally extended trajectory. We propose Model-Based Many-Actions (MBMA), an approach leveraging dynamics models for many-actions sampling in the context of SPG. MBMA addresses issues associated with existing implementations of many-actions SPG and yields lower bias and comparable variance to SPG estimated from states in model-simulated rollouts. We find that MBMA bias and variance structure matches that predicted by theory. As a result, MBMA achieves improved sample efficiency and higher returns on a range of continuous action environments as compared to model-free, many-actions, and model-based on-policy SPG baselines.

Function calling capabilities are crucial for deploying Large Language Models in real-world applications, yet current training approaches fail to develop robust reasoning strategies. Supervised fine-tuning produces models that rely on superficial pattern matching, while standard reinforcement learning methods struggle with the complex action space of structured function calls. We present a novel reinforcement learning framework designed to enhance group relative policy optimization through strategic entropy based exploration specifically tailored for function calling tasks. Our approach addresses three critical challenges in function calling: insufficient exploration during policy learning, lack of structured reasoning in chain-of-thought generation, and inadequate verification of parameter extraction. Our two-stage data preparation pipeline ensures high-quality training samples through iterative LLM evaluation and abstract syntax tree validation. Extensive experiments on the Berkeley Function Calling Leaderboard demonstrate that this framework achieves state-of-the-art performance among open-source models with 86.02\% overall accuracy, outperforming standard GRPO by up to 6\% on complex multi-function scenarios. Notably, our method shows particularly strong improvements on code-pretrained models, suggesting that structured language generation capabilities provide an advantageous starting point for reinforcement learning in function calling tasks. We will release all the code, models and dataset to benefit the community.

Recently, Masked Diffusion Models (MDMs) have shown promising potential across vision, language, and cross-modal generation. However, a notable discrepancy exists between their training and inference procedures. In particular, MDM inference is a multi-step, iterative process governed not only by the model itself but also by various schedules that dictate the token-decoding trajectory (e.g., how many tokens to decode at each step). In contrast, MDMs are typically trained using a simplified, single-step BERT-style objective that masks a subset of tokens and predicts all of them simultaneously. This step-level simplification fundamentally disconnects the training paradigm from the trajectory-level nature of inference, leaving the inference schedules never optimized during training. In this paper, we introduce Co-GRPO, which reformulates MDM generation as a unified Markov Decision Process (MDP) that jointly incorporates both the model and the inference schedule. By applying Group Relative Policy Optimization at the trajectory level, Co-GRPO cooperatively optimizes model parameters and schedule parameters under a shared reward, without requiring costly backpropagation through the multi-step generation process. This holistic optimization aligns training with inference more thoroughly and substantially improves generation quality. Empirical results across four benchmarks-ImageReward, HPS, GenEval, and DPG-Bench-demonstrate the effectiveness of our approach. For more details, please refer to our project page: https://co-grpo.github.io/ .

Adapting Large Language Models (LLMs) for agent tasks is critical in developing language agents. Direct Preference Optimization (DPO) is a promising technique for this adaptation with the alleviation of compounding errors, offering a means to directly optimize Reinforcement Learning (RL) objectives. However, applying DPO to multi-turn tasks presents challenges due to the inability to cancel the partition function. Overcoming this obstacle involves making the partition function independent of the current state and addressing length disparities between preferred and dis-preferred trajectories. In this light, we replace the policy constraint with the state-action occupancy measure constraint in the RL objective and add length normalization to the Bradley-Terry model, yielding a novel loss function named DMPO for multi-turn agent tasks with theoretical explanations. Extensive experiments on three multi-turn agent task datasets confirm the effectiveness and superiority of the DMPO loss. The code is available at https://github.com/swt-user/DMPO.

In multi-agent reinforcement learning, the behaviors that agents learn in a single Markov Game (MG) are typically confined to the given agent number. Every single MG induced by varying the population may possess distinct optimal joint strategies and game-specific knowledge, which are modeled independently in modern multi-agent reinforcement learning algorithms. In this work, our focus is on creating agents that can generalize across population-varying MGs. Instead of learning a unimodal policy, each agent learns a policy set comprising effective strategies across a variety of games. To achieve this, we propose Meta Representations for Agents (MRA) that explicitly models the game-common and game-specific strategic knowledge. By representing the policy sets with multi-modal latent policies, the game-common strategic knowledge and diverse strategic modes are discovered through an iterative optimization procedure. We prove that by approximately maximizing the resulting constrained mutual information objective, the policies can reach Nash Equilibrium in every evaluation MG when the latent space is sufficiently large. When deploying MRA in practical settings with limited latent space sizes, fast adaptation can be achieved by leveraging the first-order gradient information. Extensive experiments demonstrate the effectiveness of MRA in improving training performance and generalization ability in challenging evaluation games.

Policy optimization methods are powerful algorithms in Reinforcement Learning (RL) for their flexibility to deal with policy parameterization and ability to handle model misspecification. However, these methods usually suffer from slow convergence rates and poor sample complexity. Hence it is important to design provably sample efficient algorithms for policy optimization. Yet, recent advances for this problems have only been successful in tabular and linear setting, whose benign structures cannot be generalized to non-linearly parameterized policies. In this paper, we address this problem by leveraging recent advances in value-based algorithms, including bounded eluder-dimension and online sensitivity sampling, to design a low-switching sample-efficient policy optimization algorithm, LPO, with general non-linear function approximation. We show that, our algorithm obtains an varepsilon-optimal policy with only O(text{poly(d)}{varepsilon^3}) samples, where varepsilon is the suboptimality gap and d is a complexity measure of the function class approximating the policy. This drastically improves previously best-known sample bound for policy optimization algorithms, O(text{poly(d)}{varepsilon^8}). Moreover, we empirically test our theory with deep neural nets to show the benefits of the theoretical inspiration.

Policy optimization methods with function approximation are widely used in multi-agent reinforcement learning. However, it remains elusive how to design such algorithms with statistical guarantees. Leveraging a multi-agent performance difference lemma that characterizes the landscape of multi-agent policy optimization, we find that the localized action value function serves as an ideal descent direction for each local policy. Motivated by the observation, we present a multi-agent PPO algorithm in which the local policy of each agent is updated similarly to vanilla PPO. We prove that with standard regularity conditions on the Markov game and problem-dependent quantities, our algorithm converges to the globally optimal policy at a sublinear rate. We extend our algorithm to the off-policy setting and introduce pessimism to policy evaluation, which aligns with experiments. To our knowledge, this is the first provably convergent multi-agent PPO algorithm in cooperative Markov games.

Large language models (LLMs) excel at general mathematical reasoning but fail catastrophically on specialized technical mathematics. In wireless communications, where problems require precise manipulation of information-theoretic bounds, optimization constraints, and signal processing formulations, even state-of-the-art models struggle to achieve competent performance. We present WirelessMathLM, demonstrating that compact models (0.5B-7B parameters) can match or exceed much larger models through domain-specific reinforcement learning with verifiable rewards. Our key insight is that wireless mathematics problems possess a unique property--verifiable correctness--that enables effective reinforcement learning without human feedback. We construct WirelessMathBench-XL, a comprehensive benchmark of 4,027 problems from 970 papers. Using Group Relative Policy Optimization (GRPO) with binary verification rewards, we train models directly from base checkpoints without supervised warm-start. Our 7B model achieves 39.5% accuracy on WirelessMathBench-XL, approaching GPT-4o (40.4%) while using about 100 times fewer parameters than DeepSeek-R1 (671B, 57.4%). Remarkably, GRPO training nearly doubles performance across all model scales (0.5B +11%, 3B +103%, 7B +81%), with positive transfer to general mathematics benchmarks--our models gain +8.4 points on average across MATH, Minerva-Math, OlympiadBench, AMC, and AIME without any training on these tasks.

Existing tool-augmented large language models (LLMs) encounter significant challenges when processing complex queries. Current frameworks such as ReAct are prone to local optimization traps due to their reliance on incremental decision-making processes. To address these limitations, we propose a novel Planner-centric Plan-Execute paradigm that fundamentally resolves local optimization bottlenecks through architectural innovation. Central to our approach is a novel Planner model that performs global Directed Acyclic Graph (DAG) planning for complex queries, enabling optimized execution beyond conventional tool coordination. We also introduce ComplexTool-Plan, a large-scale benchmark dataset featuring complex queries that demand sophisticated multi-tool composition and coordination capabilities. Additionally, we develop a two-stage training methodology that integrates Supervised Fine-Tuning (SFT) with Group Relative Policy Optimization (GRPO), systematically enhancing the Planner's tool selection accuracy and global planning awareness through structured DAG-based planning. When integrated with a capable executor, our framework achieves state-of-the-art performance on the StableToolBench benchmark for complex user queries, demonstrating superior end-to-end execution capabilities and robust handling of intricate multi-tool workflows.

Reinforcement learning (RL) provides a principled framework for improving Vision-Language Models (VLMs) on complex reasoning tasks. However, existing RL approaches often rely on human-annotated labels or task-specific heuristics to define verifiable rewards, both of which are costly and difficult to scale. We introduce VisPlay, a self-evolving RL framework that enables VLMs to autonomously improve their reasoning abilities using large amounts of unlabeled image data. Starting from a single base VLM, VisPlay assigns the model into two interacting roles: an Image-Conditioned Questioner that formulates challenging yet answerable visual questions, and a Multimodal Reasoner that generates silver responses. These roles are jointly trained with Group Relative Policy Optimization (GRPO), which incorporates diversity and difficulty rewards to balance the complexity of generated questions with the quality of the silver answers. VisPlay scales efficiently across two model families. When trained on Qwen2.5-VL and MiMo-VL, VisPlay achieves consistent improvements in visual reasoning, compositional generalization, and hallucination reduction across eight benchmarks, including MM-Vet and MMMU, demonstrating a scalable path toward self-evolving multimodal intelligence. The project page is available at https://bruno686.github.io/VisPlay/

Reinforcement learning (RL) has become central to enhancing reasoning in large language models (LLMs). Yet on-policy algorithms such as Group Relative Policy Optimization (GRPO) often suffer in early training: noisy gradients from low-quality rollouts lead to unstable updates and inefficient exploration. We introduce Slow-Fast Policy Optimization (SFPO), a simple yet efficient framework to address these limitations via decomposing each step into three stages: a short fast trajectory of inner steps on the same batch, a reposition mechanism to control off-policy drift, and a final slow correction. This reposition-before-update design preserves the objective and rollout process unchanged, making SFPO plug-compatible with existing policy-gradient pipelines. Extensive experiments demonstrate that SFPO consistently improves stability, reduces rollouts, and accelerates convergence of reasoning RL training. Specifically, it outperforms GRPO by up to 2.80 points in average on math reasoning benchmarks. It also achieves up to 4.93 fewer rollouts and a 4.19 reduction in wall-clock time to match GRPO's best accuracy.

Large Language Models (LLMs) have demonstrated remarkable capabilities, enabling language agents to excel at single-turn tasks. However, their application to complex, multi-step, and long-horizon tasks remains challenging. While reinforcement learning (RL) offers a promising avenue for addressing these challenges, mainstream approaches typically rely solely on sparse, outcome-based rewards, a limitation that becomes especially problematic for group-based RL algorithms lacking critic models, such as Group Relative Policy Optimization (GRPO). In such methods, uniformly rewarding or penalizing all actions within a trajectory can lead to training instability and suboptimal policies, because beneficial and detrimental actions are often entangled across multi-step interactions. To address this challenge, we propose SALT, a novel and lightweight framework that provides a finer-grained advantage assignment, derived solely from outcome rewards. We achieve this by constructing a graph from trajectories of the same prompt, which allows us to quantify the quality of each step and assign advantages accordingly. Crucially, SALT is designed as a plug-and-play module that seamlessly integrates with existing group-based RL algorithms, requiring no modifications to the rollout procedure and introducing negligible computational overhead. Extensive experiments on the WebShop, ALFWorld, and AppWorld benchmarks with various model sizes demonstrate that SALT consistently improves performance. We also conduct a thorough analysis to validate the design choices behind SALT and offer actionable insights.

Large language model (LLM) agents need to perform multi-turn interactions in real-world tasks. However, existing multi-turn RL algorithms for optimizing LLM agents fail to perform effective credit assignment over multiple turns while leveraging the generalization capabilities of LLMs and it remains unclear how to develop such algorithms. To study this, we first introduce a new benchmark, ColBench, where an LLM agent interacts with a human collaborator over multiple turns to solve realistic tasks in backend programming and frontend design. Building on this benchmark, we propose a novel RL algorithm, SWEET-RL (RL with Step-WisE Evaluation from Training-time information), that uses a carefully designed optimization objective to train a critic model with access to additional training-time information. The critic provides step-level rewards for improving the policy model. Our experiments demonstrate that SWEET-RL achieves a 6% absolute improvement in success and win rates on ColBench compared to other state-of-the-art multi-turn RL algorithms, enabling Llama-3.1-8B to match or exceed the performance of GPT4-o in realistic collaborative content creation.

Model-free reinforcement learning algorithms have seen remarkable progress, but key challenges remain. Trust Region Policy Optimization (TRPO) is known for ensuring monotonic policy improvement through conservative updates within a trust region, backed by strong theoretical guarantees. However, its reliance on complex second-order optimization limits its practical efficiency. Proximal Policy Optimization (PPO) addresses this by simplifying TRPO's approach using ratio clipping, improving efficiency but sacrificing some theoretical robustness. This raises a natural question: Can we combine the strengths of both methods? In this paper, we introduce Simple Policy Optimization (SPO), a novel unconstrained first-order algorithm. By slightly modifying the policy loss used in PPO, SPO can achieve the best of both worlds. Our new objective improves upon ratio clipping, offering stronger theoretical properties and better constraining the probability ratio within the trust region. Empirical results demonstrate that SPO outperforms PPO with a simple implementation, particularly for training large, complex network architectures end-to-end.

Recent advances in large language models (LLMs) have demonstrated remarkable capabilities across diverse domains, particularly in mathematical reasoning, amid which geometry problem solving remains a challenging area where auxiliary construction plays a enssential role. Existing approaches either achieve suboptimal performance or rely on massive LLMs (e.g., GPT-4o), incurring massive computational costs. We posit that reinforcement learning with verifiable reward (e.g., GRPO) offers a promising direction for training smaller models that effectively combine auxiliary construction with robust geometric reasoning. However, directly applying GRPO to geometric reasoning presents fundamental limitations due to its dependence on unconditional rewards, which leads to indiscriminate and counterproductive auxiliary constructions. To address these challenges, we propose Group Contrastive Policy Optimization (GCPO), a novel reinforcement learning framework featuring two key innovations: (1) Group Contrastive Masking, which adaptively provides positive or negative reward signals for auxiliary construction based on contextual utility, and a (2) length reward that promotes longer reasoning chains. Building on GCPO, we develop GeometryZero, a family of affordable-size geometric reasoning models that judiciously determine when to employ auxiliary construction. Our extensive empirical evaluation across popular geometric benchmarks (Geometry3K, MathVista) demonstrates that GeometryZero models consistently outperform baselines (e.g. GRPO), achieving an average improvement of 4.29% across all benchmarks.

Large language models (LLMs) exhibit varying levels of confidence across input prompts (questions): some lead to consistent, semantically similar answers, while others yield diverse or contradictory outputs. This variation reflects LLM's uncertainty about the input prompt, a signal of how confidently the model understands a given problem. However, vanilla Group Relative Policy Optimization (GRPO) treats all prompts equally during policy updates, ignoring this important information about the model's knowledge boundaries. To address this limitation, we propose SEED-GRPO (Semantic Entropy EnhanceD GRPO), which explicitly measures LLMs' uncertainty of the input prompts semantic entropy. Semantic entropy measures the diversity of meaning in multiple generated answers given a prompt and uses this to modulate the magnitude of policy updates. This uncertainty-aware training mechanism enables dynamic adjustment of policy update magnitudes based on question uncertainty. It allows more conservative updates on high-uncertainty questions while maintaining the original learning signal on confident ones. Experimental results on five mathematical reasoning benchmarks (AIME24 56.7, AMC 68.7, MATH 83.4, Minerva 34.2, and OlympiadBench 48.0) demonstrate that SEED-GRPO achieves new state-of-the-art performance in average accuracy, validating the effectiveness of uncertainty-aware policy optimization.

Multi-agent systems (MAS) and reinforcement learning (RL) are widely used to enhance the agentic capabilities of large language models (LLMs). MAS improves task performance through role-based orchestration, while RL uses environmental rewards to learn stronger policies, such as GRPO-style optimization. However, applying on-policy RL to MAS remains underexplored and presents unique challenges. Algorithmically, standard GRPO grouping assumptions break down because prompts vary by role and by turn. System-wise, the training stack must support MAS-workflow rollouts and on-policy updates for both single-policy and multi-policy models. We propose AT-GRPO, which includes (i) an agent- and turn-wise grouped RL algorithm tailored to MAS and (ii) a training system that supports both single- and multi-policy regimes. Across game, planning, coding, and math tasks, AT-GRPO delivers substantial gains. On long-horizon planning, it increases accuracy from a 14.0 to 47.0 percent single-agent RL baseline to 96.0 to 99.5 percent. It also improves reasoning performance, with average gains of 3.87 to 7.62 percent on coding tasks and 9.0 to 17.93 percent on math. Code and environments are available at: https://github.com/pettingllms-ai/PettingLLMs.

A broad use case of large language models (LLMs) is in goal-directed decision-making tasks (or "agent" tasks), where an LLM needs to not just generate completions for a given prompt, but rather make intelligent decisions over a multi-turn interaction to accomplish a task (e.g., when interacting with the web, using tools, or providing customer support). Reinforcement learning (RL) provides a general paradigm to address such agent tasks, but current RL methods for LLMs largely focus on optimizing single-turn rewards. By construction, most single-turn RL methods cannot endow LLMs with the ability to intelligently seek information over multiple turns, perform credit assignment, or reason about their past actions -- all of which are critical in agent tasks. This raises the question: how can we design effective and efficient multi-turn RL algorithms for LLMs? In this paper, we develop a framework for building multi-turn RL algorithms for fine-tuning LLMs, that preserves the flexibility of existing single-turn RL methods for LLMs (e.g., proximal policy optimization), while accommodating multiple turns, long horizons, and delayed rewards effectively. To do this, our framework adopts a hierarchical RL approach and runs two RL algorithms in parallel: a high-level off-policy value-based RL algorithm to aggregate reward over utterances, and a low-level RL algorithm that utilizes this high-level value function to train a token policy within each utterance or turn. Our hierarchical framework, Actor-Critic Framework with a Hierarchical Structure (ArCHer), can also give rise to other RL methods. Empirically, we find that ArCHer significantly improves efficiency and performance on agent tasks, attaining a sample efficiency of about 100x over existing methods, while also improving with larger model capacity (upto the 7 billion scale that we tested on).

Recent advancements in Large Language Models(LLMs) have demonstrated their capabilities not only in reasoning but also in invoking external tools, particularly search engines. However, teaching models to discern when to invoke search and when to rely on their internal knowledge remains a significant challenge. Existing reinforcement learning approaches often lead to redundant search behaviors, resulting in inefficiencies and over-cost. In this paper, we propose SEM, a novel post-training reinforcement learning framework that explicitly trains LLMs to optimize search usage. By constructing a balanced dataset combining MuSiQue and MMLU, we create scenarios where the model must learn to distinguish between questions it can answer directly and those requiring external retrieval. We design a structured reasoning template and employ Group Relative Policy Optimization(GRPO) to post-train the model's search behaviors. Our reward function encourages accurate answering without unnecessary search while promoting effective retrieval when needed. Experimental results demonstrate that our method significantly reduces redundant search operations while maintaining or improving answer accuracy across multiple challenging benchmarks. This framework advances the model's reasoning efficiency and extends its capability to judiciously leverage external knowledge.

Large Reasoning Models (LRMs) have achieved remarkable success, yet they often suffer from producing unnecessary and verbose reasoning chains. We identify a core aspect of this issue as "invalid thinking" -- models tend to repeatedly double-check their work after having derived the correct answer. To address this specific inefficiency, we move beyond the general principles of Efficacy and Efficiency to propose two new, fine-grained principles: Brevity, which advocates for eliminating redundancy, and Sufficiency, which ensures critical reasoning steps are preserved. Guided by these principles, we introduce LC-R1, a post-training method based on Group Relative Policy Optimization (GRPO). LC-R1 employs a novel combination of a Length Reward for overall conciseness and a Compress Reward that is specifically designed to remove the invalid portion of the thinking process. Extensive experiments on multiple reasoning benchmarks demonstrate that LC-R1 achieves a significant reduction in sequence length (~50%) with only a marginal (~2%) drop in accuracy, achieving a favorable trade-off point on the Pareto frontier that prioritizes high compression. Our analysis further validates the robustness of LC-R1 and provides valuable insights for developing more powerful yet computationally efficient LRMs. Our code is released at https://github.com/zxiangx/LC-R1.

Reinforcement learning is emerging as a primary driver for improving language model reasoning capabilities. A fundamental question is whether current reinforcement learning algorithms -- such as Group Relative Policy Optimization (GRPO), the de facto standard algorithm used to improve language model reasoning -- merely sharpen the base model's distribution around problems it can already solve. We investigate this question in the context of formal theorem proving, which has access to a perfect verifier. We identify a degenerate rank bias in GRPO in which highly probable trajectories are reinforced and rare ones are neglected. This results in distribution sharpening: the model can solve some problems with fewer samples, but underperforms simply sampling more solutions from the original model. To overcome GRPO's rank bias we introduce unlikeliness reward, a simple method for explicitly up-weighting rare but correct solutions. We show that unlikeliness reward mitigates rank bias and improves pass@N across a large range of N in both synthetic and real theorem proving settings. We also uncover an unexpected link between rank bias and a seemingly mundane hyperparameter -- the number of updates per batch -- that leads to a second, complementary mitigation. We combine our insights into a revised GRPO training recipe for formal theorem proving, yielding an open pipeline that achieves competitive performance to DeepSeek-Prover-V1.5-RL on the miniF2F-test benchmark. We release our implementation at https://github.com/AndreHe02/rewarding-unlikely-release

Large Language Models (LLMs) have achieved remarkable success at tasks like summarization that involve a single turn of interaction. However, they can still struggle with multi-turn tasks like dialogue that require long-term planning. Previous works on multi-turn dialogue extend single-turn reinforcement learning from human feedback (RLHF) methods to the multi-turn setting by treating all prior dialogue turns as a long context. Such approaches suffer from covariate shift: the conversations in the training set have previous turns generated by some reference policy, which means that low training error may not necessarily correspond to good performance when the learner is actually in the conversation loop. In response, we introduce REgressing the RELative FUture (REFUEL), an efficient policy optimization approach designed to address multi-turn RLHF in LLMs. REFUEL employs a single model to estimate Q-values and trains on self-generated data, addressing the covariate shift issue. REFUEL frames the multi-turn RLHF problem as a sequence of regression tasks on iteratively collected datasets, enabling ease of implementation. Theoretically, we prove that REFUEL can match the performance of any policy covered by the training set. Empirically, we evaluate our algorithm by using Llama-3.1-70B-it to simulate a user in conversation with our model. REFUEL consistently outperforms state-of-the-art methods such as DPO and REBEL across various settings. Furthermore, despite having only 8 billion parameters, Llama-3-8B-it fine-tuned with REFUEL outperforms Llama-3.1-70B-it on long multi-turn dialogues. Implementation of REFUEL can be found at https://github.com/ZhaolinGao/REFUEL/, and models trained by REFUEL can be found at https://huggingface.co/Cornell-AGI.

Combinatorial Optimization underpins many real-world applications and yet, designing performant algorithms to solve these complex, typically NP-hard, problems remains a significant research challenge. Reinforcement Learning (RL) provides a versatile framework for designing heuristics across a broad spectrum of problem domains. However, despite notable progress, RL has not yet supplanted industrial solvers as the go-to solution. Current approaches emphasize pre-training heuristics that construct solutions but often rely on search procedures with limited variance, such as stochastically sampling numerous solutions from a single policy or employing computationally expensive fine-tuning of the policy on individual problem instances. Building on the intuition that performant search at inference time should be anticipated during pre-training, we propose COMPASS, a novel RL approach that parameterizes a distribution of diverse and specialized policies conditioned on a continuous latent space. We evaluate COMPASS across three canonical problems - Travelling Salesman, Capacitated Vehicle Routing, and Job-Shop Scheduling - and demonstrate that our search strategy (i) outperforms state-of-the-art approaches on 11 standard benchmarking tasks and (ii) generalizes better, surpassing all other approaches on a set of 18 procedurally transformed instance distributions.

Developing AI agents that can robustly adapt to dramatically different strategic landscapes without retraining is a central challenge for multi-agent learning. Pok\'emon Video Game Championships (VGC) is a domain with an extraordinarily large space of possible team configurations of approximately 10^{139} - far larger than those of Dota or Starcraft. The highly discrete, combinatorial nature of team building in Pok\'emon VGC causes optimal strategies to shift dramatically depending on both the team being piloted and the opponent's team, making generalization uniquely challenging. To advance research on this problem, we introduce VGC-Bench: a benchmark that provides critical infrastructure, standardizes evaluation protocols, and supplies human-play datasets and a range of baselines - from large-language-model agents and behavior cloning to reinforcement learning and empirical game-theoretic methods such as self-play, fictitious play, and double oracle. In the restricted setting where an agent is trained and evaluated on a single-team configuration, our methods are able to win against a professional VGC competitor. We extensively evaluated all baseline methods over progressively larger team sets and find that even the best-performing algorithm in the single-team setting struggles at scaling up as team size grows. Thus, policy generalization across diverse team strategies remains an open challenge for the community. Our code is open sourced at https://github.com/cameronangliss/VGC-Bench.

In this work, we address the task of table image to LaTeX code generation, with the goal of automating the reconstruction of high-quality, publication-ready tables from visual inputs. A central challenge of this task lies in accurately handling complex tables -- those with large sizes, deeply nested structures, and semantically rich or irregular cell content -- where existing methods often fail. We begin with a comprehensive analysis, identifying key challenges and highlighting the limitations of current evaluation protocols. To overcome these issues, we propose a reinforced multimodal large language model (MLLM) framework, where a pre-trained MLLM is fine-tuned on a large-scale table-to-LaTeX dataset. To further improve generation quality, we introduce a dual-reward reinforcement learning strategy based on Group Relative Policy Optimization (GRPO). Unlike standard approaches that optimize purely over text outputs, our method incorporates both a structure-level reward on LaTeX code and a visual fidelity reward computed from rendered outputs, enabling direct optimization of the visual output quality. We adopt a hybrid evaluation protocol combining TEDS-Structure and CW-SSIM, and show that our method achieves state-of-the-art performance, particularly on structurally complex tables, demonstrating the effectiveness and robustness of our approach.

In this work, we investigate the application of Taylor expansions in reinforcement learning. In particular, we propose Taylor expansion policy optimization, a policy optimization formalism that generalizes prior work (e.g., TRPO) as a first-order special case. We also show that Taylor expansions intimately relate to off-policy evaluation. Finally, we show that this new formulation entails modifications which improve the performance of several state-of-the-art distributed algorithms.

Recent advances in R1-like reasoning models leveraging Group Relative Policy Optimization (GRPO) have significantly improved the performance of language models on mathematical reasoning tasks. However, current GRPO implementations encounter critical challenges, including reward sparsity due to binary accuracy metrics, limited incentives for conciseness, and insufficient focus on complex reasoning tasks. To address these issues, we propose GRPO-LEAD, a suite of novel enhancements tailored for mathematical reasoning. Specifically, GRPO-LEAD introduces (1) a length-dependent accuracy reward to encourage concise and precise solutions, (2) an explicit penalty mechanism for incorrect answers to sharpen decision boundaries, and (3) a difficulty-aware advantage reweighting strategy that amplifies learning signals for challenging problems. Furthermore, we systematically examine the impact of model scale and supervised fine-tuning (SFT) strategies, demonstrating that larger-scale base models and carefully curated datasets significantly enhance reinforcement learning effectiveness. Extensive empirical evaluations and ablation studies confirm that GRPO-LEAD substantially mitigates previous shortcomings, resulting in language models that produce more concise, accurate, and robust reasoning across diverse mathematical tasks.

Despite the success of neural-based combinatorial optimization methods for end-to-end heuristic learning, out-of-distribution generalization remains a challenge. In this paper, we present a novel formulation of Combinatorial Optimization Problems (COPs) as Markov Decision Processes (MDPs) that effectively leverages common symmetries of COPs to improve out-of-distribution robustness. Starting from a direct MDP formulation of a constructive method, we introduce a generic way to reduce the state space, based on Bisimulation Quotienting (BQ) in MDPs. Then, for COPs with a recursive nature, we specialize the bisimulation and show how the reduced state exploits the symmetries of these problems and facilitates MDP solving. Our approach is principled and we prove that an optimal policy for the proposed BQ-MDP actually solves the associated COPs. We illustrate our approach on five classical problems: the Euclidean and Asymmetric Traveling Salesman, Capacitated Vehicle Routing, Orienteering and Knapsack Problems. Furthermore, for each problem, we introduce a simple attention-based policy network for the BQ-MDPs, which we train by imitation of (near) optimal solutions of small instances from a single distribution. We obtain new state-of-the-art results for the five COPs on both synthetic and realistic benchmarks. Notably, in contrast to most existing neural approaches, our learned policies show excellent generalization performance to much larger instances than seen during training, without any additional search procedure.

Adapting large language models (LLMs) for specific tasks usually involves fine-tuning through reinforcement learning with human feedback (RLHF) on preference data. While these data often come from diverse labelers' groups (e.g., different demographics, ethnicities, company teams, etc.), traditional RLHF approaches adopt a "one-size-fits-all" approach, i.e., they indiscriminately assume and optimize a single preference model, thus not being robust to unique characteristics and needs of the various groups. To address this limitation, we propose a novel Group Robust Preference Optimization (GRPO) method to align LLMs to individual groups' preferences robustly. Our approach builds upon reward-free direct preference optimization methods, but unlike previous approaches, it seeks a robust policy which maximizes the worst-case group performance. To achieve this, GRPO adaptively and sequentially weights the importance of different groups, prioritizing groups with worse cumulative loss. We theoretically study the feasibility of GRPO and analyze its convergence for the log-linear policy class. By fine-tuning LLMs with GRPO using diverse group-based global opinion data, we significantly improved performance for the worst-performing groups, reduced loss imbalances across groups, and improved probability accuracies compared to non-robust baselines.

We present a two-stage fine-tuning approach to make the large language model Qwen3 14B "think" natively in Korean. In the first stage, supervised fine-tuning (SFT) on a high-quality Korean reasoning dataset establishes a strong foundation in Korean logical reasoning, yielding notable improvements in Korean-language tasks and even some gains in general reasoning ability. In the second stage, we employ reinforcement learning with a customized Group Relative Policy Optimization (GRPO) algorithm to further enhance both Korean reasoning alignment and overall problem-solving performance. We address critical stability challenges in GRPO training - such as reward hacking and policy collapse - by introducing an oracle judge model that calibrates the reward signal. Our approach achieves stable learning (avoiding the collapse observed in naive GRPO) and leads to steady, incremental performance gains. The final RL-tuned model demonstrates substantially improved results on advanced reasoning benchmarks (particularly math and coding tasks) while maintaining knowledge and language proficiency, successfully conducting its internal chain-of-thought entirely in Korean.

This paper introduces TempSamp-R1, a new reinforcement fine-tuning framework designed to improve the effectiveness of adapting multimodal large language models (MLLMs) to video temporal grounding tasks. We reveal that existing reinforcement learning methods, such as Group Relative Policy Optimization (GRPO), rely on on-policy sampling for policy updates. However, in tasks with large temporal search spaces, this strategy becomes both inefficient and limited in performance, as it often fails to identify temporally accurate solutions. To address this limitation, TempSamp-R1 leverages ground-truth annotations as off-policy supervision to provide temporally precise guidance, effectively compensating for the sparsity and misalignment in on-policy solutions. To further stabilize training and reduce variance in reward-based updates, TempSamp-R1 provides a non-linear soft advantage computation method that dynamically reshapes the reward feedback via an asymmetric transformation. By employing a hybrid Chain-of-Thought (CoT) training paradigm, TempSamp-R1 optimizes a single unified model to support both CoT and non-CoT inference modes, enabling efficient handling of queries with varying reasoning complexity. Experimental results demonstrate that TempSamp-R1 outperforms GRPO-based baselines, establishing new state-of-the-art performance on benchmark datasets: Charades-STA (R1@0.7: 52.9%, +2.7%), ActivityNet Captions (R1@0.5: 56.0%, +5.3%), and QVHighlights (mAP: 30.0%, +3.0%). Moreover, TempSamp-R1 shows robust few-shot generalization capabilities under limited data. Code: https://github.com/HVision-NKU/TempSamp-R1

Provably efficient Model-Based Reinforcement Learning (MBRL) based on optimism or posterior sampling (PSRL) is ensured to attain the global optimality asymptotically by introducing the complexity measure of the model. However, the complexity might grow exponentially for the simplest nonlinear models, where global convergence is impossible within finite iterations. When the model suffers a large generalization error, which is quantitatively measured by the model complexity, the uncertainty can be large. The sampled model that current policy is greedily optimized upon will thus be unsettled, resulting in aggressive policy updates and over-exploration. In this work, we propose Conservative Dual Policy Optimization (CDPO) that involves a Referential Update and a Conservative Update. The policy is first optimized under a reference model, which imitates the mechanism of PSRL while offering more stability. A conservative range of randomness is guaranteed by maximizing the expectation of model value. Without harmful sampling procedures, CDPO can still achieve the same regret as PSRL. More importantly, CDPO enjoys monotonic policy improvement and global optimality simultaneously. Empirical results also validate the exploration efficiency of CDPO.

Designing control policies whose performance level is guaranteed to remain above a given threshold in a span of environments is a critical feature for the adoption of reinforcement learning (RL) in real-world applications. The search for such robust policies is a notoriously difficult problem, related to the so-called dynamic model of transition function uncertainty, where the environment dynamics are allowed to change at each time step. But in practical cases, one is rather interested in robustness to a span of static transition models throughout interaction episodes. The static model is known to be harder to solve than the dynamic one, and seminal algorithms, such as robust value iteration, as well as most recent works on deep robust RL, build upon the dynamic model. In this work, we propose to revisit the static model. We suggest an analysis of why solving the static model under some mild hypotheses is a reasonable endeavor, based on an equivalence with the dynamic model, and formalize the general intuition that robust MDPs can be solved by tackling a series of static problems. We introduce a generic meta-algorithm called IWOCS, which incrementally identifies worst-case transition models so as to guide the search for a robust policy. Discussion on IWOCS sheds light on new ways to decouple policy optimization and adversarial transition functions and opens new perspectives for analysis. We derive a deep RL version of IWOCS and demonstrate it is competitive with state-of-the-art algorithms on classical benchmarks.

We propose a decentralized, learning-based framework for dynamic coalition formation in Multi-Robot Task Allocation (MRTA). Our approach extends Multi-Agent Proximal Policy Optimization (MAPPO) by integrating spatial action maps, robot motion planning, intention sharing, and task allocation revision to enable effective and adaptive coalition formation. Extensive simulation studies confirm the effectiveness of our model, enabling each robot to rely solely on local information to learn timely revisions of task selections and form coalitions with other robots to complete collaborative tasks. Additionally, our model significantly outperforms existing methods, including a market-based baseline. Furthermore, we evaluate the scalability and generalizability of the proposed framework, highlighting its ability to handle large robot populations and adapt to scenarios featuring diverse task sets.

We describe an iterative procedure for optimizing policies, with guaranteed monotonic improvement. By making several approximations to the theoretically-justified procedure, we develop a practical algorithm, called Trust Region Policy Optimization (TRPO). This algorithm is similar to natural policy gradient methods and is effective for optimizing large nonlinear policies such as neural networks. Our experiments demonstrate its robust performance on a wide variety of tasks: learning simulated robotic swimming, hopping, and walking gaits; and playing Atari games using images of the screen as input. Despite its approximations that deviate from the theory, TRPO tends to give monotonic improvement, with little tuning of hyperparameters.

Recent work on enhancing the reasoning abilities of large language models (LLMs) has introduced explicit length control as a means of constraining computational cost while preserving accuracy. However, existing approaches rely on fixed-length training budgets, which do not take advantage of the natural progression from exploration to compression during learning. In this work, we propose a curriculum learning strategy for length-controlled reasoning using Group Relative Policy Optimization (GRPO). Our method starts with generous token budgets and gradually tightens them over training, encouraging models to first discover effective solution strategies and then distill them into more concise reasoning traces. We augment GRPO with a reward function that balances three signals: task correctness (via verifier feedback), length efficiency, and formatting adherence (via structural tags). Experiments on GSM8K, MATH500, SVAMP, College Math, and GSM+ demonstrate that curriculum-based training consistently outperforms fixed-budget baselines at the same final budget, achieving higher accuracy and significantly improved token efficiency. We further ablate the impact of reward weighting and decay schedule design, showing that progressive constraint serves as a powerful inductive bias for training efficient reasoning models. Our code and checkpoints are released at: https://github.com/hammoudhasan/curriculum_grpo.

On-policy reinforcement learning (RL), particularly Proximal Policy Optimization (PPO) and Group Relative Policy Optimization (GRPO), has become the dominant paradigm for fine-tuning large language models (LLMs). While policy ratio clipping stabilizes training, this heuristic hard constraint incurs a fundamental cost: it indiscriminately truncates gradients from high-return yet high-divergence actions, suppressing rare but highly informative "eureka moments" in complex reasoning. Moreover, once data becomes slightly stale, hard clipping renders it unusable, leading to severe sample inefficiency. In this work, we revisit the trust-region objective in policy optimization and show that explicitly constraining the variance (second central moment) of the policy ratio provides a principled and smooth relaxation of hard clipping. This distributional constraint stabilizes policy updates while preserving gradient signals from valuable trajectories. Building on this insight, we propose R^2VPO (Ratio-Variance Regularized Policy Optimization), a novel primal-dual framework that supports stable on-policy learning and enables principled off-policy data reuse by dynamically reweighting stale samples rather than discarding them. We extensively evaluate R^2VPO on fine-tuning state-of-the-art LLMs, including DeepSeek-Distill-Qwen-1.5B and the openPangu-Embedded series (1B and 7B), across challenging mathematical reasoning benchmarks. Experimental results show that R^2VPO consistently achieves superior asymptotic performance, with average relative gains of up to 17% over strong clipping-based baselines, while requiring approximately 50% fewer rollouts to reach convergence. These findings establish ratio-variance control as a promising direction for improving both stability and data efficiency in RL-based LLM alignment.