Daily Papers

Reasoning language models (RLMs), also known as Large Reasoning Models (LRMs), such as OpenAI's o1 and o3, DeepSeek-V3, and Alibaba's QwQ, have redefined AI's problem-solving capabilities by extending large language models (LLMs) with advanced reasoning mechanisms. Yet, their high costs, proprietary nature, and complex architectures - uniquely combining Reinforcement Learning (RL), search heuristics, and LLMs - present accessibility and scalability challenges. To address these, we propose a comprehensive blueprint that organizes RLM components into a modular framework, based on a survey and analysis of all RLM works. This blueprint incorporates diverse reasoning structures (chains, trees, graphs, and nested forms), reasoning strategies (e.g., Monte Carlo Tree Search, Beam Search), RL concepts (policy, value models and others), and supervision schemes (Output-Based and Process-Based Supervision). We also provide detailed mathematical formulations and algorithmic specifications to simplify RLM implementation. By showing how schemes like LLaMA-Berry, QwQ, Journey Learning, and Graph of Thoughts fit as special cases, we demonstrate the blueprint's versatility and unifying potential. To illustrate its utility, we introduce x1, a modular implementation for rapid RLM prototyping and experimentation. Using x1 and a literature review, we provide key insights, such as multi-phase training for policy and value models, and the importance of familiar training distributions. Finally, we outline how RLMs can integrate with a broader LLM ecosystem, including tools and databases. Our work demystifies RLM construction, democratizes advanced reasoning capabilities, and fosters innovation, aiming to mitigate the gap between "rich AI" and "poor AI" by lowering barriers to RLM development and experimentation.

Recently, test-time scaling Large Language Models (LLMs) have demonstrated exceptional reasoning capabilities across scientific and professional tasks by generating long chains-of-thought (CoT). As a crucial component for developing these reasoning models, reinforcement learning (RL), exemplified by Proximal Policy Optimization (PPO) and its variants, allows models to learn through trial and error. However, PPO can be time-consuming due to its inherent on-policy nature, which is further exacerbated by increasing response lengths. In this work, we propose Truncated Proximal Policy Optimization (T-PPO), a novel extension to PPO that improves training efficiency by streamlining policy update and length-restricted response generation. T-PPO mitigates the issue of low hardware utilization, an inherent drawback of fully synchronized long-generation procedures, where resources often sit idle during the waiting periods for complete rollouts. Our contributions are two-folds. First, we propose Extended Generalized Advantage Estimation (EGAE) for advantage estimation derived from incomplete responses while maintaining the integrity of policy learning. Second, we devise a computationally optimized mechanism that allows for the independent optimization of the policy and value models. By selectively filtering prompt and truncated tokens, this mechanism reduces redundant computations and accelerates the training process without sacrificing convergence performance. We demonstrate the effectiveness and efficacy of T-PPO on AIME 2024 with a 32B base model. The experimental results show that T-PPO improves the training efficiency of reasoning LLMs by up to 2.5x and outperforms its existing competitors.

Recent advancements in large language models (LLMs) have substantially enhanced their mathematical reasoning abilities. However, these models still struggle with complex problems that require multiple reasoning steps, frequently leading to logical or numerical errors. While numerical mistakes can be largely addressed by integrating a code interpreter, identifying logical errors within intermediate steps is more challenging. Moreover, manually annotating these steps for training is not only expensive but also labor-intensive, requiring the expertise of professional annotators. In our study, we introduce an innovative approach that bypasses the need for process annotations (from human or GPTs) by utilizing the Monte Carlo Tree Search (MCTS) framework. This technique automatically generates both the process supervision and the step-level evaluation signals. Our method iteratively trains the policy and value models, leveraging the capabilities of a well-pretrained LLM to progressively enhance its mathematical reasoning skills. Furthermore, we propose an efficient inference strategy-step-level beam search, where the value model is crafted to assist the policy model (i.e., LLM) in navigating more effective reasoning paths, rather than solely relying on prior probabilities. The experimental results on both in-domain and out-of-domain datasets demonstrate that even without GPT-4 or human-annotated process supervision, our AlphaMath framework achieves comparable or superior results to previous state-of-the-art methods.

Reinforcement Learning (RL) mathematically formulates decision-making with Markov Decision Process (MDP). With MDPs, researchers have achieved remarkable breakthroughs across various domains, including games, robotics, and language models. This paper seeks a new possibility, Natural Language Reinforcement Learning (NLRL), by extending traditional MDP to natural language-based representation space. Specifically, NLRL innovatively redefines RL principles, including task objectives, policy, value function, Bellman equation, and policy iteration, into their language counterparts. With recent advancements in large language models (LLMs), NLRL can be practically implemented to achieve RL-like policy and value improvement by either pure prompting or gradient-based training. Experiments over Maze, Breakthrough, and Tic-Tac-Toe games demonstrate the effectiveness, efficiency, and interpretability of the NLRL framework among diverse use cases. Our code will be released at https://github.com/waterhorse1/Natural-language-RL.

Improving the multi-step reasoning ability of large language models (LLMs) with offline reinforcement learning (RL) is essential for quickly adapting them to complex tasks. While Direct Preference Optimization (DPO) has shown promise in aligning LLMs with human preferences, it is less suitable for multi-step reasoning tasks because (1) DPO relies on paired preference data, which is not readily available for multi-step reasoning tasks, and (2) it treats all tokens uniformly, making it ineffective for credit assignment in multi-step reasoning tasks, which often come with sparse reward. In this work, we propose OREO (Offline Reasoning Optimization), an offline RL method for enhancing LLM multi-step reasoning. Building on insights from previous works of maximum entropy reinforcement learning, it jointly learns a policy model and value function by optimizing the soft Bellman Equation. We show in principle that it reduces the need to collect pairwise data and enables better credit assignment. Empirically, OREO surpasses existing offline learning methods on multi-step reasoning benchmarks, including mathematical reasoning tasks (GSM8K, MATH) and embodied agent control (ALFWorld). The approach can be extended to a multi-iteration framework when additional resources are available. Furthermore, the learned value function can be leveraged to guide the tree search for free, which can further boost performance during test time.

Large, general-purpose robotic policies trained on diverse demonstration datasets have been shown to be remarkably effective both for controlling a variety of robots in a range of different scenes, and for acquiring broad repertoires of manipulation skills. However, the data that such policies are trained on is generally of mixed quality -- not only are human-collected demonstrations unlikely to perform the task perfectly, but the larger the dataset is, the harder it is to curate only the highest quality examples. It also remains unclear how optimal data from one embodiment is for training on another embodiment. In this paper, we present a general and broadly applicable approach that enhances the performance of such generalist robot policies at deployment time by re-ranking their actions according to a value function learned via offline RL. This approach, which we call Value-Guided Policy Steering (V-GPS), is compatible with a wide range of different generalist policies, without needing to fine-tune or even access the weights of the policy. We show that the same value function can improve the performance of five different state-of-the-art policies with different architectures, even though they were trained on distinct datasets, attaining consistent performance improvement on multiple robotic platforms across a total of 12 tasks. Code and videos can be found at: https://nakamotoo.github.io/V-GPS

Reinforcement Learning from Human Feedback (RLHF) has proven effective in aligning large language models with human intentions, yet it often relies on complex methodologies like Proximal Policy Optimization (PPO) that require extensive hyper-parameter tuning and present challenges in sample efficiency and stability. In this paper, we introduce Inverse-Q*, an innovative framework that transcends traditional RL methods by optimizing token-level reinforcement learning without the need for additional reward or value models. Inverse-Q* leverages direct preference optimization techniques but extends them by estimating the conditionally optimal policy directly from the model's responses, facilitating more granular and flexible policy shaping. Our approach reduces reliance on human annotation and external supervision, making it especially suitable for low-resource settings. We present extensive experimental results demonstrating that Inverse-Q* not only matches but potentially exceeds the effectiveness of PPO in terms of convergence speed and the alignment of model responses with human preferences. Our findings suggest that Inverse-Q* offers a practical and robust alternative to conventional RLHF approaches, paving the way for more efficient and adaptable model training approaches.

Large language models (LLMs) provide excellent text-generation capabilities, but standard prompting and generation methods generally do not lead to intentional or goal-directed agents and might necessitate considerable prompt tuning. This becomes particularly apparent in multi-turn conversations: even the best current LLMs rarely ask clarifying questions, engage in explicit information gathering, or take actions now that lead to better decisions after multiple turns. Reinforcement learning has the potential to leverage the powerful modeling capabilities of LLMs, as well as their internal representation of textual interactions, to create capable goal-directed language agents. This can enable intentional and temporally extended interactions, such as with humans, through coordinated persuasion and carefully crafted questions, or in goal-directed play through text games to bring about desired final outcomes. However, enabling this requires the community to develop stable and reliable reinforcement learning algorithms that can effectively train LLMs. Developing such algorithms requires tasks that can gauge progress on algorithm design, provide accessible and reproducible evaluations for multi-turn interactions, and cover a range of task properties and challenges in improving reinforcement learning algorithms. Our paper introduces the LMRL-Gym benchmark for evaluating multi-turn RL for LLMs, together with an open-source research framework containing a basic toolkit for getting started on multi-turn RL with offline value-based and policy-based RL methods. Our benchmark consists of 8 different language tasks, which require multiple rounds of language interaction and cover a range of tasks in open-ended dialogue and text games.

Recent methodologies in LLM self-training mostly rely on LLM generating responses and filtering those with correct output answers as training data. This approach often yields a low-quality fine-tuning training set (e.g., incorrect plans or intermediate reasoning). In this paper, we develop a reinforced self-training approach, called ReST-MCTS*, based on integrating process reward guidance with tree search MCTS* for collecting higher-quality reasoning traces as well as per-step value to train policy and reward models. ReST-MCTS* circumvents the per-step manual annotation typically used to train process rewards by tree-search-based reinforcement learning: Given oracle final correct answers, ReST-MCTS* is able to infer the correct process rewards by estimating the probability this step can help lead to the correct answer. These inferred rewards serve dual purposes: they act as value targets for further refining the process reward model and also facilitate the selection of high-quality traces for policy model self-training. We first show that the tree-search policy in ReST-MCTS* achieves higher accuracy compared with prior LLM reasoning baselines such as Best-of-N and Tree-of-Thought, within the same search budget. We then show that by using traces searched by this tree-search policy as training data, we can continuously enhance the three language models for multiple iterations, and outperform other self-training algorithms such as ReST^EM and Self-Rewarding LM.

A key challenge in applying reinforcement learning (RL) to diffusion large language models (dLLMs) lies in the intractability of their likelihood functions, which are essential for the RL objective, necessitating corresponding approximation in each training step. While existing methods approximate the log-likelihoods by their evidence lower bounds (ELBOs) via customized Monte Carlo (MC) sampling, the forward computational graphs of all MC samples need to be retained for the gradient computation of non-linear terms in the RL objective, resulting in significant memory overhead. This constraint restricts feasible sample sizes, leading to imprecise likelihood approximations and ultimately distorting the RL objective. To overcome this limitation, we propose Boundary-Guided Policy Optimization (BGPO), a memory-efficient RL algorithm that maximizes a specially constructed lower bound of the ELBO-based objective. This lower bound is carefully designed to satisfy two key properties: (1) Linearity: it is formulated in a linear sum where each term depends only on a single MC sample, thereby enabling gradient accumulation across samples and ensuring constant memory usage; (2) Equivalence: Both the value and gradient of this lower bound are equal to those of the ELBO-based objective in on-policy training, making it also an effective approximation for the original RL objective. These properties allow BGPO to adopt a large MC sample size, resulting in more accurate likelihood approximations and improved RL objective estimation, which in turn leads to enhanced performance. Experiments show that BGPO significantly outperforms previous RL algorithms for dLLMs in math problem solving, code generation, and planning tasks.

Vision-Language-Action (VLA) models have shown substantial potential in real-world robotic manipulation. However, fine-tuning these models through supervised learning struggles to achieve robust performance due to limited, inconsistent demonstrations, especially in contact-rich environments. In this paper, we propose a reinforced fine-tuning approach for VLA models, named ConRFT, which consists of offline and online fine-tuning with a unified consistency-based training objective, to address these challenges. In the offline stage, our method integrates behavior cloning and Q-learning to effectively extract policy from a small set of demonstrations and stabilize value estimating. In the online stage, the VLA model is further fine-tuned via consistency policy, with human interventions to ensure safe exploration and high sample efficiency. We evaluate our approach on eight diverse real-world manipulation tasks. It achieves an average success rate of 96.3% within 45-90 minutes of online fine-tuning, outperforming prior supervised methods with a 144% improvement in success rate and 1.9x shorter episode length. This work highlights the potential of integrating reinforcement learning to enhance the performance of VLA models for real-world robotic applications. Videos and code are available at our project website https://cccedric.github.io/conrft/.

Medical language models (MLMs) have become pivotal in advancing medical natural language processing. However, prior models that rely on pre-training or supervised fine-tuning often exhibit low data efficiency and limited practicality in real-world clinical applications. While OpenAIs O1 highlights test-time scaling in mathematics, attempts to replicate this approach in medicine typically distill responses from GPT-series models to open-source models, focusing primarily on multiple-choice tasks. This strategy, though straightforward, neglects critical concerns like data privacy and realistic deployment in clinical settings. In this work, we present a deployable, small-scale medical language model, \mone, designed for long-chain reasoning in clinical tasks using a self-evolution paradigm. Starting with a seed dataset of around 8,000 instances spanning five domains and 16 datasets, we prompt a base policy model to perform Monte Carlo Tree Search (MCTS) to construct verifiable reasoning chains. Each reasoning step is assigned an evolution rollout value, allowing verified trajectories to train the policy model and the reward model. During inference, the policy model generates multiple responses, and the reward model selects the one with the highest reward score. Experiments on eleven evaluation datasets demonstrate that \mone outperforms prior open-source models by 2 points, with the addition of the reward model further boosting performance (sim13 points), surpassing GPT-4o-mini. Code and data are available at https://github.com/pixas/MedSSS.

Efficient use of large language models (LLMs) is critical for deployment at scale: without adaptive routing, systems either overpay for strong models or risk poor performance from weaker ones. Selecting the right LLM for each query is fundamentally an online decision problem: models differ in strengths, prices fluctuate, and users value accuracy and cost differently. Yet most routers are trained offline with labels for all candidate models, an assumption that breaks in deployment, where only the outcome of the chosen model is observed. We bridge this gap with BaRP, a Bandit-feedback Routing with Preferences approach that trains under the same partial-feedback restriction as deployment, while supporting preference-tunable inference: operators can dial the performance/cost trade-off at test time without retraining. Framed as a contextual bandit over prompt features and a user preference vector, our method simulates an online feedback setting during training and adapts its routing decisions to each new prompt, rather than depending on full-information offline supervision. Comprehensive experiments show that our method consistently outperforms strong offline routers by at least 12.46% and the largest LLM by at least 2.45%, and generalizes robustly for unseen tasks.

Proximal Policy Optimization (PPO)-based Reinforcement Learning from Human Feedback (RLHF) is essential for aligning large language models (LLMs) with human preferences. It requires joint training of an actor and critic with a pretrained, fixed reward model for guidance. This approach increases computational complexity and instability due to actor-critic interdependence. Additionally, PPO lacks access to true environment rewards in LLM tasks, limiting its adaptability. Under such conditions, pretraining a value model or a reward model becomes equivalent, as both provide fixed supervisory signals without new ground-truth feedback. To address these issues, we propose Decoupled Value Policy Optimization (DVPO), a lean framework that replaces traditional reward modeling with a pretrained global value model (GVM). The GVM is conditioned on policy trajectories and predicts token-level return-to-go estimates. By decoupling value model from policy training (via frozen GVM-driven RL objectives), DVPO eliminates actor-critic interdependence, reducing GPU memory usage by 40\% and training time by 35\% compared to conventional RLHF. Experiments across benchmarks show DVPO outperforms efficient RLHF methods (e.g., DPO) while matching state-of-the-art PPO in performance.

Knowledge distillation (KD) has been shown to be highly effective in guiding a student model with a larger teacher model and achieving practical benefits in improving the computational and memory efficiency for large language models (LLMs). State-of-the-art KD methods for LLMs mostly rely on minimizing explicit distribution distance between teacher and student probability predictions. Instead of optimizing these mandatory behaviour cloning objectives, we explore an imitation learning strategy for KD of LLMs. In particular, we minimize the imitation gap by matching the action-value moments of the teacher's behavior from both on- and off-policy perspectives. To achieve this action-value moment-matching goal, we propose an adversarial training algorithm to jointly estimate the moment-matching distance and optimize the student policy to minimize it. Results from both task-agnostic instruction-following experiments and task-specific experiments demonstrate the effectiveness of our method and achieve new state-of-the-art performance.

Flow-based generative models have shown remarkable success in text-to-image generation, yet fine-tuning them with intermediate feedback remains challenging, especially for continuous-time flow matching models. Most existing approaches solely learn from outcome rewards, struggling with the credit assignment problem. Alternative methods that attempt to learn a critic via direct regression on cumulative rewards often face training instabilities and model collapse in online settings. We present AC-Flow, a robust actor-critic framework that addresses these challenges through three key innovations: (1) reward shaping that provides well-normalized learning signals to enable stable intermediate value learning and gradient control, (2) a novel dual-stability mechanism that combines advantage clipping to prevent destructive policy updates with a warm-up phase that allows the critic to mature before influencing the actor, and (3) a scalable generalized critic weighting scheme that extends traditional reward-weighted methods while preserving model diversity through Wasserstein regularization. Through extensive experiments on Stable Diffusion 3, we demonstrate that AC-Flow achieves state-of-the-art performance in text-to-image alignment tasks and generalization to unseen human preference models. Our results demonstrate that even with a computationally efficient critic model, we can robustly finetune flow models without compromising generative quality, diversity, or stability.

Inference-time alignment provides an efficient alternative for aligning LLMs with humans. However, these approaches still face challenges, such as limited scalability due to policy-specific value functions and latency during the inference phase. In this paper, we propose a novel approach, Diffusion-styled Preference Optimization (\model), which provides an efficient and policy-agnostic solution for aligning LLMs with humans. By directly performing alignment at sentence level, \model~avoids the time latency associated with token-level generation. Designed as a plug-and-play module, \model~can be seamlessly integrated with various base models to enhance their alignment. Extensive experiments on AlpacaEval 2, MT-bench, and HH-RLHF demonstrate that \model~achieves superior alignment performance across various settings, achieving a favorable trade-off between alignment quality and inference-time latency. Furthermore, \model~demonstrates model-agnostic scalability, significantly improving the performance of large models such as Llama-3-70B.

Language model pretraining with next token prediction has proved effective for scaling compute but is limited to the amount of available training data. Scaling reinforcement learning (RL) unlocks a new axis for the continued improvement of artificial intelligence, with the promise that large language models (LLMs) can scale their training data by learning to explore with rewards. However, prior published work has not produced competitive results. In light of this, we report on the training practice of Kimi k1.5, our latest multi-modal LLM trained with RL, including its RL training techniques, multi-modal data recipes, and infrastructure optimization. Long context scaling and improved policy optimization methods are key ingredients of our approach, which establishes a simplistic, effective RL framework without relying on more complex techniques such as Monte Carlo tree search, value functions, and process reward models. Notably, our system achieves state-of-the-art reasoning performance across multiple benchmarks and modalities -- e.g., 77.5 on AIME, 96.2 on MATH 500, 94-th percentile on Codeforces, 74.9 on MathVista -- matching OpenAI's o1. Moreover, we present effective long2short methods that use long-CoT techniques to improve short-CoT models, yielding state-of-the-art short-CoT reasoning results -- e.g., 60.8 on AIME, 94.6 on MATH500, 47.3 on LiveCodeBench -- outperforming existing short-CoT models such as GPT-4o and Claude Sonnet 3.5 by a large margin (up to +550%).

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).

Predicting temporal progress from visual trajectories is important for intelligent robots that can learn, adapt, and improve. However, learning such progress estimator, or temporal value function, across different tasks and domains requires both a large amount of diverse data and methods which can scale and generalize. To address these challenges, we present Generative Value Learning (\GVL), a universal value function estimator that leverages the world knowledge embedded in vision-language models (VLMs) to predict task progress. Naively asking a VLM to predict values for a video sequence performs poorly due to the strong temporal correlation between successive frames. Instead, GVL poses value estimation as a temporal ordering problem over shuffled video frames; this seemingly more challenging task encourages VLMs to more fully exploit their underlying semantic and temporal grounding capabilities to differentiate frames based on their perceived task progress, consequently producing significantly better value predictions. Without any robot or task specific training, GVL can in-context zero-shot and few-shot predict effective values for more than 300 distinct real-world tasks across diverse robot platforms, including challenging bimanual manipulation tasks. Furthermore, we demonstrate that GVL permits flexible multi-modal in-context learning via examples from heterogeneous tasks and embodiments, such as human videos. The generality of GVL enables various downstream applications pertinent to visuomotor policy learning, including dataset filtering, success detection, and advantage-weighted regression -- all without any model training or finetuning.

Despite the recent success associated with Large Language Models (LLMs), they are notably cost-prohibitive to deploy in resource-constrained environments due to their excessive memory and computational demands. In addition to model parameters, the key-value cache is also stored in GPU memory, growing linearly with batch size and sequence length. As a remedy, recent works have proposed various eviction policies for maintaining the overhead of key-value cache under a given budget. This paper embarks on the efficacy of existing eviction policies in terms of importance score calculation and eviction scope construction. We identify the deficiency of prior policies in these two aspects and introduce RoCo, a robust cache omission policy based on temporal attention scores and robustness measures. Extensive experimentation spanning prefilling and auto-regressive decoding stages validates the superiority of RoCo. Finally, we release EasyKV, a versatile software package dedicated to user-friendly key-value constrained generative inference. Code available at https://github.com/DRSY/EasyKV.

Reinforcement learning from human feedback (RLHF) has demonstrated great promise in aligning large language models (LLMs) with human preference. Depending on the availability of preference data, both online and offline RLHF are active areas of investigation. A key bottleneck is understanding how to incorporate uncertainty estimation in the reward function learned from the preference data for RLHF, regardless of how the preference data is collected. While the principles of optimism or pessimism under uncertainty are well-established in standard reinforcement learning (RL), a practically-implementable and theoretically-grounded form amenable to large language models is not yet available, as standard techniques for constructing confidence intervals become intractable under arbitrary policy parameterizations. In this paper, we introduce a unified approach to online and offline RLHF -- value-incentivized preference optimization (VPO) -- which regularizes the maximum-likelihood estimate of the reward function with the corresponding value function, modulated by a sign to indicate whether the optimism or pessimism is chosen. VPO also directly optimizes the policy with implicit reward modeling, and therefore shares a simpler RLHF pipeline similar to direct preference optimization. Theoretical guarantees of VPO are provided for both online and offline settings, matching the rates of their standard RL counterparts. Moreover, experiments on text summarization and dialog verify the practicality and effectiveness of VPO.

The recent advancements in Large Language Models (LLMs) have garnered widespread acclaim for their remarkable emerging capabilities. However, the issue of hallucination has parallelly emerged as a by-product, posing significant concerns. While some recent endeavors have been made to identify and mitigate different types of hallucination, there has been a limited emphasis on the nuanced categorization of hallucination and associated mitigation methods. To address this gap, we offer a fine-grained discourse on profiling hallucination based on its degree, orientation, and category, along with offering strategies for alleviation. As such, we define two overarching orientations of hallucination: (i) factual mirage (FM) and (ii) silver lining (SL). To provide a more comprehensive understanding, both orientations are further sub-categorized into intrinsic and extrinsic, with three degrees of severity - (i) mild, (ii) moderate, and (iii) alarming. We also meticulously categorize hallucination into six types: (i) acronym ambiguity, (ii) numeric nuisance, (iii) generated golem, (iv) virtual voice, (v) geographic erratum, and (vi) time wrap. Furthermore, we curate HallucInation eLiciTation (HILT), a publicly available dataset comprising of 75,000 samples generated using 15 contemporary LLMs along with human annotations for the aforementioned categories. Finally, to establish a method for quantifying and to offer a comparative spectrum that allows us to evaluate and rank LLMs based on their vulnerability to producing hallucinations, we propose Hallucination Vulnerability Index (HVI). We firmly believe that HVI holds significant value as a tool for the wider NLP community, with the potential to serve as a rubric in AI-related policy-making. In conclusion, we propose two solution strategies for mitigating hallucinations.

We present COS(M+O)S, a System 2-inspired framework for open-ended plot development that systematically explores the vast space of possible story expansions, enabling a 3B-parameter language model to approach the plot quality of a 70B model on select short-story tasks. The method accomplishes this by combining Monte Carlo Tree Search (MCTS), guided by a step-level value model that rewards moderate surprisal (curiosity) while penalizing incoherence, and Odds Ratio Preference Optimization (ORPO) to fine-tune the policy on high-value plot expansions. This iterative reinforcement learning loop systematically explores multiple candidate plot branches, backpropagates quality signals, and adapts the policy for faster convergence, notably shifting the policy from puzzle-based Chain-of-Thought to more character-driven storytelling. In small-scale tests with short-story prompts, 67%-77% of participants favored COS(M+O)S's highest-rated expansions over lower-rated ones, suggesting that our learned value function aligns. GPT-4o ratings further show that COS(M+O)S surpasses naive single-pass decoding from Llama 3.2 3B by 0.59 SD, coming within 0.06 SD of Llama 3.1 70B (no significant difference, p=0.93). Pairwise comparisons with o1 place COS(M+O)S 1.5 SD above the 3B baseline and find no statistically significant gap from 70B. Nevertheless, absolute story quality remains modest, constrained by the small model's capacity and limited training data.

We present VAPO, Value-based Augmented Proximal Policy Optimization framework for reasoning models., a novel framework tailored for reasoning models within the value-based paradigm. Benchmarked the AIME 2024 dataset, VAPO, built on the Qwen 32B pre-trained model, attains a state-of-the-art score of 60.4. In direct comparison under identical experimental settings, VAPO outperforms the previously reported results of DeepSeek-R1-Zero-Qwen-32B and DAPO by more than 10 points. The training process of VAPO stands out for its stability and efficiency. It reaches state-of-the-art performance within a mere 5,000 steps. Moreover, across multiple independent runs, no training crashes occur, underscoring its reliability. This research delves into long chain-of-thought (long-CoT) reasoning using a value-based reinforcement learning framework. We pinpoint three key challenges that plague value-based methods: value model bias, the presence of heterogeneous sequence lengths, and the sparsity of reward signals. Through systematic design, VAPO offers an integrated solution that effectively alleviates these challenges, enabling enhanced performance in long-CoT reasoning tasks.

With the proliferation of red-teaming strategies for Large Language Models (LLMs), the deficiency in the literature about improving the safety and robustness of LLM defense strategies is becoming increasingly pronounced. This paper introduces the LLM-based sentinel model as a plug-and-play prefix module designed to reconstruct the input prompt with just a few (<30) additional tokens, effectively reducing toxicity in responses from target LLMs. The sentinel model naturally overcomes the parameter inefficiency and limited model accessibility for fine-tuning large target models. We employ an interleaved training regimen using Proximal Policy Optimization (PPO) to optimize both red team and sentinel models dynamically, incorporating a value head-sharing mechanism inspired by the multi-agent centralized critic to manage the complex interplay between agents. Our extensive experiments across text-to-text and text-to-image demonstrate the effectiveness of our approach in mitigating toxic outputs, even when dealing with larger models like Llama-2, GPT-3.5 and Stable-Diffusion, highlighting the potential of our framework in enhancing safety and robustness in various applications.

Model-based reinforcement learning (MBRL) is a sample efficient technique to obtain control policies, yet unavoidable modeling errors often lead performance deterioration. The model in MBRL is often solely fitted to reconstruct dynamics, state observations in particular, while the impact of model error on the policy is not captured by the training objective. This leads to a mismatch between the intended goal of MBRL, enabling good policy and value learning, and the target of the loss function employed in practice, future state prediction. Naive intuition would suggest that value-aware model learning would fix this problem and, indeed, several solutions to this objective mismatch problem have been proposed based on theoretical analysis. However, they tend to be inferior in practice to commonly used maximum likelihood (MLE) based approaches. In this paper we propose the Value-gradient weighted Model Learning (VaGraM), a novel method for value-aware model learning which improves the performance of MBRL in challenging settings, such as small model capacity and the presence of distracting state dimensions. We analyze both MLE and value-aware approaches and demonstrate how they fail to account for exploration and the behavior of function approximation when learning value-aware models and highlight the additional goals that must be met to stabilize optimization in the deep learning setting. We verify our analysis by showing that our loss function is able to achieve high returns on the Mujoco benchmark suite while being more robust than maximum likelihood based approaches.

The recent breakthrough successes in machine learning are mainly attributed to scale: namely large-scale attention-based architectures and datasets of unprecedented scale. This paper investigates the impact of training at scale for chess. Unlike traditional chess engines that rely on complex heuristics, explicit search, or a combination of both, we train a 270M parameter transformer model with supervised learning on a dataset of 10 million chess games. We annotate each board in the dataset with action-values provided by the powerful Stockfish 16 engine, leading to roughly 15 billion data points. Our largest model reaches a Lichess blitz Elo of 2895 against humans, and successfully solves a series of challenging chess puzzles, without any domain-specific tweaks or explicit search algorithms. We also show that our model outperforms AlphaZero's policy and value networks (without MCTS) and GPT-3.5-turbo-instruct. A systematic investigation of model and dataset size shows that strong chess performance only arises at sufficient scale. To validate our results, we perform an extensive series of ablations of design choices and hyperparameters.

Reinforcement learning is able to solve complex sequential decision-making tasks but is currently limited by sample efficiency and required computation. To improve sample efficiency, recent work focuses on model-based RL which interleaves model learning with planning. Recent methods further utilize policy learning, value estimation, and, self-supervised learning as auxiliary objectives. In this paper we show that, surprisingly, a simple representation learning approach relying only on a latent dynamics model trained by latent temporal consistency is sufficient for high-performance RL. This applies when using pure planning with a dynamics model conditioned on the representation, but, also when utilizing the representation as policy and value function features in model-free RL. In experiments, our approach learns an accurate dynamics model to solve challenging high-dimensional locomotion tasks with online planners while being 4.1 times faster to train compared to ensemble-based methods. With model-free RL without planning, especially on high-dimensional tasks, such as the DeepMind Control Suite Humanoid and Dog tasks, our approach outperforms model-free methods by a large margin and matches model-based methods' sample efficiency while training 2.4 times faster.

Aligning Large Language Models (LLMs) to cater to different human preferences, learning new skills, and unlearning harmful behavior is an important problem. Search-based methods, such as Best-of-N or Monte-Carlo Tree Search, are performant, but impractical for LLM adaptation due to their high inference cost. On the other hand, using Reinforcement Learning (RL) for adaptation is computationally efficient, but performs worse due to the optimization challenges in co-training the value function and the policy. We present a new framework for reward optimization, Value Augmented Sampling (VAS), that can maximize different reward functions using data sampled from only the initial, frozen LLM. VAS solves for the optimal reward-maximizing policy without co-training the policy and the value function, making the optimization stable, outperforming established baselines, such as PPO and DPO, on standard benchmarks, and achieving comparable results to Best-of-128 with lower inference cost. Unlike existing RL methods that require changing the weights of the LLM, VAS does not require access to the weights of the pre-trained LLM. Thus, it can even adapt LLMs (e.g., ChatGPT), which are available only as APIs. In addition, our algorithm unlocks the new capability of composing several rewards and controlling the extent of each one during deployment time, paving the road ahead for the future of aligned, personalized LLMs.

Training Vision-Language Models (VLMs) for Graphical User Interfaces (GUI) agents via Reinforcement Learning (RL) faces critical challenges: environment-based RL requires costly interactions, while environment-free methods struggle with distribution shift and reward generalization. We propose an environment-free RL framework that decouples value estimation from policy optimization by leveraging a pretrained Value Environment Model (VEM). VEM predicts state-action values directly from offline data, distilling human-like priors about GUI interaction outcomes without requiring next-state prediction or environmental feedback. This avoids compounding errors and enhances resilience to UI changes by focusing on semantic reasoning (e.g., Does this action advance the user's goal?). The framework operates in two stages: (1) pretraining VEM to estimate long-term action utilities and (2) guiding policy exploration with frozen VEM signals, enabling layout-agnostic GUI automation. Evaluated on Android-in-the-Wild benchmarks, VEM achieves state-of-the-art performance in both offline and online settings, outperforming environment-free baselines significantly and matching environment-based approaches without interaction costs. Importantly, VEM demonstrates that semantic-aware value estimation can achieve comparable performance with online-trained methods.

Constructing agents with planning capabilities has long been one of the main challenges in the pursuit of artificial intelligence. Tree-based planning methods have enjoyed huge success in challenging domains, such as chess and Go, where a perfect simulator is available. However, in real-world problems the dynamics governing the environment are often complex and unknown. In this work we present the MuZero algorithm which, by combining a tree-based search with a learned model, achieves superhuman performance in a range of challenging and visually complex domains, without any knowledge of their underlying dynamics. MuZero learns a model that, when applied iteratively, predicts the quantities most directly relevant to planning: the reward, the action-selection policy, and the value function. When evaluated on 57 different Atari games - the canonical video game environment for testing AI techniques, in which model-based planning approaches have historically struggled - our new algorithm achieved a new state of the art. When evaluated on Go, chess and shogi, without any knowledge of the game rules, MuZero matched the superhuman performance of the AlphaZero algorithm that was supplied with the game rules.

We introduce RLang, a domain-specific language (DSL) for communicating domain knowledge to an RL agent. Unlike existing RL DSLs that ground to single elements of a decision-making formalism (e.g., the reward function or policy), RLang can specify information about every element of a Markov decision process. We define precise syntax and grounding semantics for RLang, and provide a parser that grounds RLang programs to an algorithm-agnostic partial world model and policy that can be exploited by an RL agent. We provide a series of example RLang programs demonstrating how different RL methods can exploit the resulting knowledge, encompassing model-free and model-based tabular algorithms, policy gradient and value-based methods, hierarchical approaches, and deep methods.

We study the problem of offline pre-training and online fine-tuning for reinforcement learning from high-dimensional observations in the context of realistic robot tasks. Recent offline model-free approaches successfully use online fine-tuning to either improve the performance of the agent over the data collection policy or adapt to novel tasks. At the same time, model-based RL algorithms have achieved significant progress in sample efficiency and the complexity of the tasks they can solve, yet remain under-utilized in the fine-tuning setting. In this work, we argue that existing model-based offline RL methods are not suitable for offline-to-online fine-tuning in high-dimensional domains due to issues with distribution shifts, off-dynamics data, and non-stationary rewards. We propose an on-policy model-based method that can efficiently reuse prior data through model-based value expansion and policy regularization, while preventing model exploitation by controlling epistemic uncertainty. We find that our approach successfully solves tasks from the MetaWorld benchmark, as well as the Franka Kitchen robot manipulation environment completely from images. To the best of our knowledge, MOTO is the first method to solve this environment from pixels.

Model Predictive Control (MPC) has been demonstrated to be effective in continuous control tasks. When a world model and a value function are available, planning a sequence of actions ahead of time leads to a better policy. Existing methods typically obtain the value function and the corresponding policy in a model-free manner. However, we find that such an approach struggles with complex tasks, resulting in poor policy learning and inaccurate value estimation. To address this problem, we leverage the strengths of MPC itself. In this work, we introduce Bootstrapped Model Predictive Control (BMPC), a novel algorithm that performs policy learning in a bootstrapped manner. BMPC learns a network policy by imitating an MPC expert, and in turn, uses this policy to guide the MPC process. Combined with model-based TD-learning, our policy learning yields better value estimation and further boosts the efficiency of MPC. We also introduce a lazy reanalyze mechanism, which enables computationally efficient imitation learning. Our method achieves superior performance over prior works on diverse continuous control tasks. In particular, on challenging high-dimensional locomotion tasks, BMPC significantly improves data efficiency while also enhancing asymptotic performance and training stability, with comparable training time and smaller network sizes. Code is available at https://github.com/wertyuilife2/bmpc.

Recent advancements in aligning large language models via reinforcement learning have achieved remarkable gains in solving complex reasoning problems, but at the cost of expensive on-policy rollouts and limited exploration of diverse reasoning paths. In this work, we introduce TreePO, involving a self-guided rollout algorithm that views sequence generation as a tree-structured searching process. Composed of dynamic tree sampling policy and fixed-length segment decoding, TreePO leverages local uncertainty to warrant additional branches. By amortizing computation across common prefixes and pruning low-value paths early, TreePO essentially reduces the per-update compute burden while preserving or enhancing exploration diversity. Key contributions include: (1) a segment-wise sampling algorithm that alleviates the KV cache burden through contiguous segments and spawns new branches along with an early-stop mechanism; (2) a tree-based segment-level advantage estimation that considers both global and local proximal policy optimization. and (3) analysis on the effectiveness of probability and quality-driven dynamic divergence and fallback strategy. We empirically validate the performance gain of TreePO on a set reasoning benchmarks and the efficiency saving of GPU hours from 22\% up to 43\% of the sampling design for the trained models, meanwhile showing up to 40\% reduction at trajectory-level and 35\% at token-level sampling compute for the existing models. While offering a free lunch of inference efficiency, TreePO reveals a practical path toward scaling RL-based post-training with fewer samples and less compute. Home page locates at https://m-a-p.ai/TreePO.

Inference-time search algorithms such as Monte-Carlo Tree Search (MCTS) may seem unnecessary when generating natural language text based on state-of-the-art reinforcement learning such as Proximal Policy Optimization (PPO). In this paper, we demonstrate that it is possible to get extra mileage out of PPO by integrating MCTS on top. The key idea is not to throw out the value network, a byproduct of PPO training for evaluating partial output sequences, when decoding text out of the policy network. More concretely, we present a novel value-guided decoding algorithm called PPO-MCTS, which can integrate the value network from PPO to work closely with the policy network during inference-time generation. Compared to prior approaches based on MCTS for controlled text generation, the key strength of our approach is to reduce the fundamental mismatch of the scoring mechanisms of the partial outputs between training and test. Evaluation on four text generation tasks demonstrate that PPO-MCTS greatly improves the preferability of generated text compared to the standard practice of using only the PPO policy. Our results demonstrate the promise of search algorithms even on top of the aligned language models from PPO, and the under-explored benefit of the value network.

When solving decision-making tasks, humans typically depend on information from two key sources: (1) Historical policy data, which provides interaction replay from the environment, and (2) Analytical insights in natural language form, exposing the invaluable thought process or strategic considerations. Despite this, the majority of preceding research focuses on only one source: they either use historical replay exclusively to directly learn policy or value functions, or engaged in language model training utilizing mere language corpus. In this paper, we argue that a powerful autonomous agent should cover both sources. Thus, we propose ChessGPT, a GPT model bridging policy learning and language modeling by integrating data from these two sources in Chess games. Specifically, we build a large-scale game and language dataset related to chess. Leveraging the dataset, we showcase two model examples ChessCLIP and ChessGPT, integrating policy learning and language modeling. Finally, we propose a full evaluation framework for evaluating language model's chess ability. Experimental results validate our model and dataset's effectiveness. We open source our code, model, and dataset at https://github.com/waterhorse1/ChessGPT.

Reinforcement learning (RL) tackles sequential decision-making problems by creating agents that interacts with their environment. However, existing algorithms often view these problem as static, focusing on point estimates for model parameters to maximize expected rewards, neglecting the stochastic dynamics of agent-environment interactions and the critical role of uncertainty quantification. Our research leverages the Kalman filtering paradigm to introduce a novel and scalable sampling algorithm called Langevinized Kalman Temporal-Difference (LKTD) for deep reinforcement learning. This algorithm, grounded in Stochastic Gradient Markov Chain Monte Carlo (SGMCMC), efficiently draws samples from the posterior distribution of deep neural network parameters. Under mild conditions, we prove that the posterior samples generated by the LKTD algorithm converge to a stationary distribution. This convergence not only enables us to quantify uncertainties associated with the value function and model parameters but also allows us to monitor these uncertainties during policy updates throughout the training phase. The LKTD algorithm paves the way for more robust and adaptable reinforcement learning approaches.

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.

Critic-free reinforcement learning methods, particularly group policies, have attracted considerable attention for their efficiency in complex tasks. However, these methods rely heavily on multiple sampling and comparisons within the policy to estimate advantage, which may cause the policy to fall into local optimum and increase computational cost. To address these issues, we propose PVPO, an efficient reinforcement learning method enhanced by an advantage reference anchor and data pre-sampling. Specifically, we use the reference model to rollout in advance and employ the calculated reward score as a reference anchor. Our approach effectively corrects the cumulative bias introduced by intra-group comparisons and significantly reduces reliance on the number of rollouts during training. Meanwhile, the reference model can assess sample difficulty during data pre-sampling, enabling effective selection of high-gain data to improve training efficiency. Moreover, PVPO is orthogonal to other advanced critic-free RL algorithms, making it compatible with and complementary to these methods. Experiments conducted on nine datasets across two domains demonstrate that PVPO achieves State-Of-The-Art (SOTA) performance. Our approach not only demonstrates robust generalization across multiple tasks, but also exhibits scalable performance across models of varying scales.

Safety and trustworthiness are indispensable requirements for real-world applications of AI systems using large language models (LLMs). This paper formulates human value alignment as an optimization problem of the language model policy to maximize reward under a safety constraint, and then proposes an algorithm, Stepwise Alignment for Constrained Policy Optimization (SACPO). One key idea behind SACPO, supported by theory, is that the optimal policy incorporating reward and safety can be directly obtained from a reward-aligned policy. Building on this key idea, SACPO aligns LLMs step-wise with each metric while leveraging simple yet powerful alignment algorithms such as direct preference optimization (DPO). SACPO offers several advantages, including simplicity, stability, computational efficiency, and flexibility of algorithms and datasets. Under mild assumptions, our theoretical analysis provides the upper bounds on optimality and safety constraint violation. Our experimental results show that SACPO can fine-tune Alpaca-7B better than the state-of-the-art method in terms of both helpfulness and harmlessness.

We propose a novel approach to addressing two fundamental challenges in Model-based Reinforcement Learning (MBRL): the computational expense of repeatedly finding a good policy in the learned model, and the objective mismatch between model fitting and policy computation. Our "lazy" method leverages a novel unified objective, Performance Difference via Advantage in Model, to capture the performance difference between the learned policy and expert policy under the true dynamics. This objective demonstrates that optimizing the expected policy advantage in the learned model under an exploration distribution is sufficient for policy computation, resulting in a significant boost in computational efficiency compared to traditional planning methods. Additionally, the unified objective uses a value moment matching term for model fitting, which is aligned with the model's usage during policy computation. We present two no-regret algorithms to optimize the proposed objective, and demonstrate their statistical and computational gains compared to existing MBRL methods through simulated benchmarks.

Neural-based motion planning methods have achieved remarkable progress for robotic manipulators, yet a fundamental challenge lies in simultaneously accounting for both the robot's physical shape and the surrounding environment when generating safe and feasible motions. Moreover, existing approaches often rely on simplified robot models or focus primarily on obstacle representation, which can lead to incomplete collision detection and degraded performance in cluttered scenes. To address these limitations, we propose spatial anchor-based motion policy (SAMP), a unified framework that simultaneously encodes the environment and the manipulator using signed distance field (SDF) anchored on a shared spatial grid. SAMP incorporates a dedicated robot SDF network that captures the manipulator's precise geometry, enabling collision-aware reasoning beyond coarse link approximations. These representations are fused on spatial anchors and used to train a neural motion policy that generates smooth, collision-free trajectories in the proposed efficient feature alignment strategy. Experiments conducted in both simulated and real-world environments consistently show that SAMP outperforms existing methods, delivering an 11% increase in success rate and a 7% reduction in collision rate. These results highlight the benefits of jointly modelling robot and environment geometry, demonstrating its practical value in challenging real-world environments.

Planning for goal-oriented dialogue often requires simulating future dialogue interactions and estimating task progress. Many approaches thus consider training neural networks to perform look-ahead search algorithms such as A* search and Monte Carlo Tree Search (MCTS). However, this training often requires abundant annotated data, which creates challenges when faced with noisy annotations or low-resource settings. We introduce GDP-Zero, an approach using Open-Loop MCTS to perform goal-oriented dialogue policy planning without any model training. GDP-Zero prompts a large language model to act as a policy prior, value function, user simulator, and system model during the tree search. We evaluate GDP-Zero on the goal-oriented task PersuasionForGood, and find that its responses are preferred over ChatGPT up to 59.32% of the time, and are rated more persuasive than ChatGPT during interactive evaluations.

Policy-based methods currently dominate reinforcement learning (RL) pipelines for large language model (LLM) reasoning, leaving value-based approaches largely unexplored. We revisit the classical paradigm of Bellman Residual Minimization and introduce Trajectory Bellman Residual Minimization (TBRM), an algorithm that naturally adapts this idea to LLMs, yielding a simple yet effective off-policy algorithm that optimizes a single trajectory-level Bellman objective using the model's own logits as Q-values. TBRM removes the need for critics, importance-sampling ratios, or clipping, and operates with only one rollout per prompt. We prove convergence to the near-optimal KL-regularized policy from arbitrary off-policy data via an improved change-of-trajectory-measure analysis. Experiments on standard mathematical-reasoning benchmarks show that TBRM consistently outperforms policy-based baselines, like PPO and GRPO, with comparable or lower computational and memory overhead. Our results indicate that value-based RL might be a principled and efficient alternative for enhancing reasoning capabilities in LLMs.

The robustness of legged locomotion is crucial for quadrupedal robots in challenging terrains. Recently, Reinforcement Learning (RL) has shown promising results in legged locomotion and various methods try to integrate privileged distillation, scene modeling, and external sensors to improve the generalization and robustness of locomotion policies. However, these methods are hard to handle uncertain scenarios such as abrupt terrain changes or unexpected external forces. In this paper, we consider a novel risk-sensitive perspective to enhance the robustness of legged locomotion. Specifically, we employ a distributional value function learned by quantile regression to model the aleatoric uncertainty of environments, and perform risk-averse policy learning by optimizing the worst-case scenarios via a risk distortion measure. Extensive experiments in both simulation environments and a real Aliengo robot demonstrate that our method is efficient in handling various external disturbances, and the resulting policy exhibits improved robustness in harsh and uncertain situations in legged locomotion. Videos are available at https://risk-averse-locomotion.github.io/.

Recent studies, including DeepSeek-R1 and Kimi-k1.5, have demonstrated that reinforcement learning with rule-based, binary-valued reward functions can significantly enhance the reasoning capabilities of large language models. These models primarily utilize REINFORCE-based policy optimization techniques, such as REINFORCE with baseline and group relative policy optimization (GRPO). However, a key limitation remains: current policy optimization methods either neglect reward normalization or employ static normalization strategies, which fail to adapt to the dynamic nature of policy updates during training. This may result in unstable gradient estimates and hinder training stability. To address this issue, we propose Beta Normalization Policy Optimization (BNPO), a novel policy optimization method that adaptively normalizes rewards using a Beta distribution with dynamically updated parameters. BNPO aligns the normalization with the changing policy distribution, enabling more precise and lower-variance gradient estimation, which in turn promotes stable training dynamics. We provide theoretical analysis demonstrating BNPO's variance-reducing properties and show that it generalizes both REINFORCE and GRPO under binary-valued reward settings. Furthermore, we introduce an advantage decomposition mechanism to extend BNPO's applicability to more complex reward systems. Experimental results confirm that BNPO achieves state-of-the-art performance among policy optimization methods on reasoning tasks. The code is available at https://github.com/changyi7231/BNPO.

From a first-principles perspective, it may seem odd that the strongest results in foundation model fine-tuning (FT) are achieved via a relatively complex, two-stage training procedure. Specifically, one first trains a reward model (RM) on some dataset (e.g. human preferences) before using it to provide online feedback as part of a downstream reinforcement learning (RL) procedure, rather than directly optimizing the policy parameters on the dataset via offline maximum likelihood estimation. In fact, from an information-theoretic perspective, we can only lose information via passing through a reward model and cannot create any new information via on-policy sampling. To explain this discrepancy, we scrutinize several hypotheses on the value of RL in FT through both theoretical and empirical lenses. Of the hypotheses considered, we find the most support for the explanation that on problems with a generation-verification gap, the combination of the ease of learning the relatively simple RM (verifier) from the preference data, coupled with the ability of the downstream RL procedure to then filter its search space to the subset of policies (generators) that are optimal for relatively simple verifiers is what leads to the superior performance of online FT.

In many environments only a tiny subset of all states yield high reward. In these cases, few of the interactions with the environment provide a relevant learning signal. Hence, we may want to preferentially train on those high-reward states and the probable trajectories leading to them. To this end, we advocate for the use of a backtracking model that predicts the preceding states that terminate at a given high-reward state. We can train a model which, starting from a high value state (or one that is estimated to have high value), predicts and sample for which the (state, action)-tuples may have led to that high value state. These traces of (state, action) pairs, which we refer to as Recall Traces, sampled from this backtracking model starting from a high value state, are informative as they terminate in good states, and hence we can use these traces to improve a policy. We provide a variational interpretation for this idea and a practical algorithm in which the backtracking model samples from an approximate posterior distribution over trajectories which lead to large rewards. Our method improves the sample efficiency of both on- and off-policy RL algorithms across several environments and tasks.

Reinforcement Learning with Verifiable Reward (RLVR) has significantly advanced the complex reasoning abilities of Large Language Models (LLMs). However, it struggles to break through the inherent capability boundaries of the base LLM, due to its essentially on-policy strategy coupled with LLM's immense action space and sparse reward. Critically, RLVR can lead to the capability boundary collapse, narrowing the LLM's problem-solving scope. To address this problem, we propose RL-PLUS, a novel hybrid-policy optimization approach for LLMs that synergizes internal exploitation with external data to achieve stronger reasoning capabilities and surpass the boundaries of base models. RL-PLUS integrates two core components, i.e., Multiple Importance Sampling to address distributional mismatch from external data, and Exploration-Based Advantage Function to guide the model towards high-value, unexplored reasoning paths. We provide both theoretical analysis and extensive experiments to demonstrate the superiority and generalizability of our approach. Compared with existing RLVR methods, RL-PLUS achieves 1) state-of-the-art performance on six math reasoning benchmarks; 2) superior performance on six out-of-distribution reasoning tasks; 3) consistent and significant gains across diverse model families, with average relative improvements up to 69.2\%. Moreover, the analysis of Pass@k curves indicates that RL-PLUS effectively resolves the capability boundary collapse problem.

Reinforcement learning (RL) post-training is crucial for LLM alignment and reasoning, but existing policy-based methods, such as PPO and DPO, can fall short of fixing shortcuts inherited from pre-training. In this work, we introduce Qsharp, a value-based algorithm for KL-regularized RL that guides the reference policy using the optimal regularized Q function. We propose to learn the optimal Q function using distributional RL on an aggregated online dataset. Unlike prior value-based baselines that guide the model using unregularized Q-values, our method is theoretically principled and provably learns the optimal policy for the KL-regularized RL problem. Empirically, Qsharp outperforms prior baselines in math reasoning benchmarks while maintaining a smaller KL divergence to the reference policy. Theoretically, we establish a reduction from KL-regularized RL to no-regret online learning, providing the first bounds for deterministic MDPs under only realizability. Thanks to distributional RL, our bounds are also variance-dependent and converge faster when the reference policy has small variance. In sum, our results highlight Qsharp as an effective approach for post-training LLMs, offering both improved performance and theoretical guarantees. The code can be found at https://github.com/jinpz/q_sharp.

Offline reinforcement learning (RL) is a compelling framework for learning optimal policies from past experiences without additional interaction with the environment. Nevertheless, offline RL inevitably faces the problem of distributional shifts, where the states and actions encountered during policy execution may not be in the training dataset distribution. A common solution involves incorporating conservatism into the policy or the value function to safeguard against uncertainties and unknowns. In this work, we focus on achieving the same objectives of conservatism but from a different perspective. We propose COmpositional COnservatism with Anchor-seeking (COCOA) for offline RL, an approach that pursues conservatism in a compositional manner on top of the transductive reparameterization (Netanyahu et al., 2023), which decomposes the input variable (the state in our case) into an anchor and its difference from the original input. Our COCOA seeks both in-distribution anchors and differences by utilizing the learned reverse dynamics model, encouraging conservatism in the compositional input space for the policy or value function. Such compositional conservatism is independent of and agnostic to the prevalent behavioral conservatism in offline RL. We apply COCOA to four state-of-the-art offline RL algorithms and evaluate them on the D4RL benchmark, where COCOA generally improves the performance of each algorithm. The code is available at https://github.com/runamu/compositional-conservatism.

This manuscript gives a big-picture, up-to-date overview of the field of (deep) reinforcement learning and sequential decision making, covering value-based RL, policy-gradient methods, model-based methods, and various other topics (including a very brief discussion of RL+LLMs).

We give an overview of recent exciting achievements of deep reinforcement learning (RL). We discuss six core elements, six important mechanisms, and twelve applications. We start with background of machine learning, deep learning and reinforcement learning. Next we discuss core RL elements, including value function, in particular, Deep Q-Network (DQN), policy, reward, model, planning, and exploration. After that, we discuss important mechanisms for RL, including attention and memory, unsupervised learning, transfer learning, multi-agent RL, hierarchical RL, and learning to learn. Then we discuss various applications of RL, including games, in particular, AlphaGo, robotics, natural language processing, including dialogue systems, machine translation, and text generation, computer vision, neural architecture design, business management, finance, healthcare, Industry 4.0, smart grid, intelligent transportation systems, and computer systems. We mention topics not reviewed yet, and list a collection of RL resources. After presenting a brief summary, we close with discussions. Please see Deep Reinforcement Learning, arXiv:1810.06339, for a significant update.

Inverse reinforcement learning (IRL) aims to infer an agent's preferences (represented as a reward function R) from their behaviour (represented as a policy pi). To do this, we need a behavioural model of how pi relates to R. In the current literature, the most common behavioural models are optimality, Boltzmann-rationality, and causal entropy maximisation. However, the true relationship between a human's preferences and their behaviour is much more complex than any of these behavioural models. This means that the behavioural models are misspecified, which raises the concern that they may lead to systematic errors if applied to real data. In this paper, we analyse how sensitive the IRL problem is to misspecification of the behavioural model. Specifically, we provide necessary and sufficient conditions that completely characterise how the observed data may differ from the assumed behavioural model without incurring an error above a given threshold. In addition to this, we also characterise the conditions under which a behavioural model is robust to small perturbations of the observed policy, and we analyse how robust many behavioural models are to misspecification of their parameter values (such as e.g.\ the discount rate). Our analysis suggests that the IRL problem is highly sensitive to misspecification, in the sense that very mild misspecification can lead to very large errors in the inferred reward function.

Deep reinforcement learning (RL) has shown remarkable success in complex domains, however, the inherent black box nature of deep neural network policies raises significant challenges in understanding and trusting the decision-making processes. While existing explainable RL methods provide local insights, they fail to deliver a global understanding of the model, particularly in high-stakes applications. To overcome this limitation, we propose a novel model-agnostic approach that bridges the gap between explainability and interpretability by leveraging Shapley values to transform complex deep RL policies into transparent representations. The proposed approach offers two key contributions: a novel approach employing Shapley values to policy interpretation beyond local explanations and a general framework applicable to off-policy and on-policy algorithms. We evaluate our approach with three existing deep RL algorithms and validate its performance in two classic control environments. The results demonstrate that our approach not only preserves the original models' performance but also generates more stable interpretable policies.

We utilize an offline reinforcement learning (RL) model for sequential targeted promotion in the presence of budget constraints in a real-world business environment. In our application, the mobile app aims to boost customer retention by sending cash bonuses to customers and control the costs of such cash bonuses during each time period. To achieve the multi-task goal, we propose the Budget Constrained Reinforcement Learning for Sequential Promotion (BCRLSP) framework to determine the value of cash bonuses to be sent to users. We first find out the target policy and the associated Q-values that maximizes the user retention rate using an RL model. A linear programming (LP) model is then added to satisfy the constraints of promotion costs. We solve the LP problem by maximizing the Q-values of actions learned from the RL model given the budget constraints. During deployment, we combine the offline RL model with the LP model to generate a robust policy under the budget constraints. Using both online and offline experiments, we demonstrate the efficacy of our approach by showing that BCRLSP achieves a higher long-term customer retention rate and a lower cost than various baselines. Taking advantage of the near real-time cost control method, the proposed framework can easily adapt to data with a noisy behavioral policy and/or meet flexible budget constraints.

The soft-thinking paradigm for Large Language Model (LLM) reasoning can outperform the conventional discrete-token Chain-of-Thought (CoT) reasoning in some scenarios, underscoring its research and application value. However, while the discrete-token CoT reasoning pattern can be reinforced through policy optimization algorithms such as group relative policy optimization (GRPO), extending the soft-thinking pattern with Reinforcement Learning (RL) remains challenging. This difficulty stems from the complexities of injecting stochasticity into soft-thinking tokens and updating soft-thinking policies accordingly. As a result, previous attempts to combine soft-thinking with GRPO typically underperform their discrete-token GRPO counterparts. To fully unlock the potential of soft-thinking, this paper presents a novel policy optimization algorithm, SofT-GRPO, to reinforce LLMs under the soft-thinking reasoning pattern. SofT-GRPO injects the Gumbel noise into logits, employs the Gumbel-Softmax technique to avoid soft-thinking tokens outside the pre-trained embedding space, and leverages the reparameterization trick in policy gradient. We conduct experiments across base LLMs ranging from 1.5B to 7B parameters, and results demonstrate that SofT-GRPO enables soft-thinking LLMs to slightly outperform discrete-token GRPO on Pass@1 (+0.13% on average accuracy), while exhibiting a substantial uplift on Pass@32 (+2.19% on average accuracy). Codes and weights are available on https://github.com/zz1358m/SofT-GRPO-master