Daily Papers

Large language models (LLMs) have significantly advanced in reasoning tasks through reinforcement learning (RL) optimization, achieving impressive capabilities across various challenging benchmarks. However, our empirical analysis reveals a critical drawback: reasoning-oriented RL fine-tuning significantly increases the prevalence of hallucinations. We theoretically analyze the RL training dynamics, identifying high-variance gradient, entropy-induced randomness, and susceptibility to spurious local optima as key factors leading to hallucinations. To address this drawback, we propose Factuality-aware Step-wise Policy Optimization (FSPO), an innovative RL fine-tuning algorithm incorporating explicit factuality verification at each reasoning step. FSPO leverages automated verification against given evidence to dynamically adjust token-level advantage values, incentivizing factual correctness throughout the reasoning process. Experiments across mathematical reasoning and hallucination benchmarks using Qwen2.5 and Llama models demonstrate that FSPO effectively reduces hallucinations while enhancing reasoning accuracy, substantially improving both reliability and performance.

Alignment is a standard procedure to fine-tune pre-trained large language models (LLMs) to follow natural language instructions and serve as helpful AI assistants. We have observed, however, that the conventional alignment process fails to enhance the factual accuracy of LLMs, and often leads to the generation of more false facts (i.e. hallucination). In this paper, we study how to make the LLM alignment process more factual, by first identifying factors that lead to hallucination in both alignment steps:\ supervised fine-tuning (SFT) and reinforcement learning (RL). In particular, we find that training the LLM on new knowledge or unfamiliar texts can encourage hallucination. This makes SFT less factual as it trains on human labeled data that may be novel to the LLM. Furthermore, reward functions used in standard RL can also encourage hallucination, because it guides the LLM to provide more helpful responses on a diverse set of instructions, often preferring longer and more detailed responses. Based on these observations, we propose factuality-aware alignment, comprised of factuality-aware SFT and factuality-aware RL through direct preference optimization. Experiments show that our proposed factuality-aware alignment guides LLMs to output more factual responses while maintaining instruction-following capability.

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.

Large reasoning models improve with more test-time computation, but often overthink, producing unnecessarily long chains-of-thought that raise cost without improving accuracy. Prior reinforcement learning approaches typically rely on a single outcome reward with trajectory-level length penalties, which cannot distinguish essential from redundant reasoning steps and therefore yield blunt compression. Although recent work incorporates step-level signals, such as offline pruning, supervised data construction, or verifier-based intermediate rewards, reasoning length is rarely treated as an explicit step-level optimization objective during RL. We propose Step-wise Adaptive Penalization (SWAP), a fine-grained framework that allocates length reduction across steps based on intrinsic contribution. We estimate step importance from the model's on-policy log-probability improvement toward the correct answer, then treat excess length as a penalty mass redistributed to penalize low-importance steps more heavily while preserving high-importance reasoning. We optimize with a unified outcome-process advantage within group-relative policy optimization. Extensive experiments demonstrate that SWAP reduces reasoning length by 64.3% on average while improving accuracy by 5.7% relative to the base model.

Efficient multi-hop reasoning requires Large Language Models (LLMs) based agents to acquire high-value external knowledge iteratively. Previous work has explored reinforcement learning (RL) to train LLMs to perform search-based document retrieval, achieving notable improvements in QA performance, but underperform on complex, multi-hop QA resulting from the sparse rewards from global signal only. To address this gap in existing research, we introduce StepSearch, a framework for search LLMs that trained with step-wise proximal policy optimization method. It consists of richer and more detailed intermediate search rewards and token-level process supervision based on information gain and redundancy penalties to better guide each search step. We constructed a fine-grained question-answering dataset containing sub-question-level search trajectories based on open source datasets through a set of data pipeline method. On standard multi-hop QA benchmarks, it significantly outperforms global-reward baselines, achieving 11.2% and 4.2% absolute improvements for 3B and 7B models over various search with RL baselines using only 19k training data, demonstrating the effectiveness of fine-grained, stepwise supervision in optimizing deep search LLMs. Our code will be released on https://github.com/Zillwang/StepSearch.

Personalized large language models (LLMs) adapt model behavior to individual users to enhance user satisfaction, yet personalization can inadvertently distort factual reasoning. We show that when personalized LLMs face factual queries, there exists a phenomenon where the model generates answers aligned with a user's prior history rather than the objective truth, resulting in personalization-induced hallucinations that degrade factual reliability and may propagate incorrect beliefs, due to representational entanglement between personalization and factual representations. To address this issue, we propose Factuality-Preserving Personalized Steering (FPPS), a lightweight inference-time approach that mitigates personalization-induced factual distortions while preserving personalized behavior. We further introduce PFQABench, the first benchmark designed to jointly evaluate factual and personalized question answering under personalization. Experiments across multiple LLM backbones and personalization methods show that FPPS substantially improves factual accuracy while maintaining personalized performance.

Discovering achievements with a hierarchical structure in procedurally generated environments presents a significant challenge. This requires an agent to possess a broad range of abilities, including generalization and long-term reasoning. Many prior methods have been built upon model-based or hierarchical approaches, with the belief that an explicit module for long-term planning would be advantageous for learning hierarchical dependencies. However, these methods demand an excessive number of environment interactions or large model sizes, limiting their practicality. In this work, we demonstrate that proximal policy optimization (PPO), a simple yet versatile model-free algorithm, outperforms previous methods when optimized with recent implementation practices. Moreover, we find that the PPO agent can predict the next achievement to be unlocked to some extent, albeit with limited confidence. Based on this observation, we introduce a novel contrastive learning method, called achievement distillation, which strengthens the agent's ability to predict the next achievement. Our method exhibits a strong capacity for discovering hierarchical achievements and shows state-of-the-art performance on the challenging Crafter environment in a sample-efficient manner while utilizing fewer model parameters.

Recent studies generally enhance MLLMs' reasoning capabilities via supervised fine-tuning on high-quality chain-of-thought reasoning data, which often leads models to merely imitate successful reasoning paths without understanding what the wrong reasoning paths are. In this work, we aim to enhance the MLLMs' reasoning ability beyond passively imitating positive reasoning paths. To this end, we design Step-wise Group Relative Policy Optimization (StepGRPO), a new online reinforcement learning framework that enables MLLMs to self-improve reasoning ability via simple, effective and dense step-wise rewarding. Specifically, StepGRPO introduces two novel rule-based reasoning rewards: Step-wise Reasoning Accuracy Reward (StepRAR) and Step-wise Reasoning Validity Reward (StepRVR). StepRAR rewards the reasoning paths that contain necessary intermediate reasoning steps via a soft key-step matching technique, while StepRAR rewards reasoning paths that follow a well-structured and logically consistent reasoning process through a reasoning completeness and logic evaluation strategy. With the proposed StepGRPO, we introduce R1-VL, a series of MLLMs with outstanding capabilities in step-by-step reasoning. Extensive experiments over 8 benchmarks demonstrate the superiority of our methods.

Preference alignment methods such as RLHF and Direct Preference Optimization (DPO) improve instruction following, but they can also reinforce hallucinations when preference judgments reward fluency and confidence over factual correctness. We introduce F-DPO (Factuality-aware Direct Preference Optimization), a simple extension of DPO that uses only binary factuality labels. F-DPO (i) applies a label-flipping transformation that corrects misordered preference pairs so the chosen response is never less factual than the rejected one, and (ii) adds a factuality-aware margin that emphasizes pairs with clear correctness differences, while reducing to standard DPO when both responses share the same factuality. We construct factuality-aware preference data by augmenting DPO pairs with binary factuality indicators and synthetic hallucinated variants. Across seven open-weight LLMs (1B-14B), F-DPO consistently improves factuality and reduces hallucination rates relative to both base models and standard DPO. On Qwen3-8B, F-DPO reduces hallucination rates by five times (from 0.424 to 0.084) while improving factuality scores by 50 percent (from 5.26 to 7.90). F-DPO also generalizes to out-of-distribution benchmarks: on TruthfulQA, Qwen2.5-14B achieves plus 17 percent MC1 accuracy (0.500 to 0.585) and plus 49 percent MC2 accuracy (0.357 to 0.531). F-DPO requires no auxiliary reward model, token-level annotations, or multi-stage training.

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.

Flow-based generative models, including diffusion models, excel at modeling continuous distributions in high-dimensional spaces. In this work, we introduce Flow Policy Optimization (FPO), a simple on-policy reinforcement learning algorithm that brings flow matching into the policy gradient framework. FPO casts policy optimization as maximizing an advantage-weighted ratio computed from the conditional flow matching loss, in a manner compatible with the popular PPO-clip framework. It sidesteps the need for exact likelihood computation while preserving the generative capabilities of flow-based models. Unlike prior approaches for diffusion-based reinforcement learning that bind training to a specific sampling method, FPO is agnostic to the choice of diffusion or flow integration at both training and inference time. We show that FPO can train diffusion-style policies from scratch in a variety of continuous control tasks. We find that flow-based models can capture multimodal action distributions and achieve higher performance than Gaussian policies, particularly in under-conditioned settings.

Recent advances in large reasoning models have leveraged reinforcement learning with verifiable rewards (RLVR) to improve reasoning capabilities. However, scaling these methods typically requires extensive rollout computation and large datasets, leading to high training costs and low data efficiency. To mitigate this issue, we propose DEPO, a Data-Efficient Policy Optimization pipeline that combines optimized strategies for both offline and online data selection. In the offline phase, we curate a high-quality subset of training samples based on diversity, influence, and appropriate difficulty. During online RLVR training, we introduce a sample-level explorability metric to dynamically filter samples with low exploration potential, thereby reducing substantial rollout computational costs. Furthermore, we incorporate a replay mechanism for under-explored samples to ensure adequate training, which enhances the model's final convergence performance. Experiments across five reasoning benchmarks show that DEPO consistently outperforms existing methods in both offline and online data selection scenarios. Notably, using only 20% of the training data, our approach achieves a 1.85 times speed-up on AIME24 and a 1.66 times speed-up on AIME25 compared to GRPO trained on the full dataset.

Few-step diffusion models enable efficient high-resolution image synthesis but struggle to align with specific downstream objectives due to limitations of existing reinforcement learning (RL) methods in low-step regimes with limited state spaces and suboptimal sample quality. To address this, we propose Stepwise Diffusion Policy Optimization (SDPO), a novel RL framework tailored for few-step diffusion models. SDPO introduces a dual-state trajectory sampling mechanism, tracking both noisy and predicted clean states at each step to provide dense reward feedback and enable low-variance, mixed-step optimization. For further efficiency, we develop a latent similarity-based dense reward prediction strategy to minimize costly dense reward queries. Leveraging these dense rewards, SDPO optimizes a dense reward difference learning objective that enables more frequent and granular policy updates. Additional refinements, including stepwise advantage estimates, temporal importance weighting, and step-shuffled gradient updates, further enhance long-term dependency, low-step priority, and gradient stability. Our experiments demonstrate that SDPO consistently delivers superior reward-aligned results across diverse few-step settings and tasks. Code is available at https://github.com/ZiyiZhang27/sdpo.

Reinforcement Learning from Verifiable Rewards (RLVR) has emerged as a powerful paradigm for enhancing the complex reasoning capabilities of Large Reasoning Models. However, standard outcome-based supervision suffers from a critical limitation that penalizes trajectories that are largely correct but fail due to several missteps as heavily as completely erroneous ones. This coarse feedback signal causes the model to discard valuable largely correct rollouts, leading to a degradation in rollout diversity that prematurely narrows the exploration space. Process Reward Models have demonstrated efficacy in providing reliable step-wise verification for test-time scaling, naively integrating these signals into RLVR as dense rewards proves ineffective.Prior methods attempt to introduce off-policy guided whole-trajectory replacement that often outside the policy model's distribution, but still fail to utilize the largely correct rollouts generated by the model itself and thus do not effectively mitigate the narrowing of the exploration space. To address these issues, we propose SCOPE (Step-wise Correction for On-Policy Exploration), a novel framework that utilizes Process Reward Models to pinpoint the first erroneous step in suboptimal rollouts and applies fine-grained, step-wise off-policy rectification. By applying precise refinement on partially correct rollout, our method effectively salvages partially correct trajectories and increases diversity score by 13.5%, thereby sustaining a broad exploration space. Extensive experiments demonstrate that our approach establishes new state-of-the-art results, achieving an average accuracy of 46.6% on math reasoning and exhibiting robust generalization with 53.4% accuracy on out-of-distribution reasoning tasks.

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.

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.

We propose Process-Aware Policy Optimization (PAPO), a method that integrates process-level evaluation into Group Relative Policy Optimization (GRPO) through decoupled advantage normalization, to address two limitations of existing reward designs. Outcome reward models (ORM) evaluate only final-answer correctness, treating all correct responses identically regardless of reasoning quality, and gradually lose the advantage signal as groups become uniformly correct. Process reward models (PRM) offer richer supervision, but directly using PRM scores causes reward hacking, where models exploit verbosity to inflate scores while accuracy collapses. PAPO resolves both by composing the advantage from an outcome component Aout, derived from ORM and normalized over all responses, and a process component Aproc, derived from a rubric-based PRM and normalized exclusively among correct responses. This decoupled design ensures that Aout anchors training on correctness while Aproc differentiates reasoning quality without distorting the outcome signal. Experiments across multiple model scales and six benchmarks demonstrate that PAPO consistently outperforms ORM, reaching 51.3% vs.\ 46.3% on OlympiadBench while continuing to improve as ORM plateaus and declines.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a promising paradigm for enhancing the reasoning capabilities of large language models (LLMs). In this context, models explore reasoning trajectories and exploit rollouts with correct answers as positive signals for policy optimization. However, these rollouts might involve flawed patterns such as answer-guessing and jump-in-reasoning. Such flawed-positive rollouts are rewarded identically to fully correct ones, causing policy models to internalize these unreliable reasoning patterns. In this work, we first conduct a systematic study of flawed-positive rollouts in RL and find that they enable rapid capability gains during the early optimization stage, while constraining reasoning capability later by reinforcing unreliable patterns. Building on these insights, we propose Flawed-Aware Policy Optimization (FAPO), which presents a parameter-free reward penalty for flawed-positive rollouts, enabling the policy to leverage them as useful shortcuts in the warm-up stage, securing stable early gains, while gradually shifting optimization toward reliable reasoning in the later refinement stage. To accurately and comprehensively detect flawed-positive rollouts, we introduce a generative reward model (GenRM) with a process-level reward that precisely localizes reasoning errors. Experiments show that FAPO is effective in broad domains, improving outcome correctness, process reliability, and training stability without increasing the token budget.

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.

We propose a new family of policy gradient methods for reinforcement learning, which alternate between sampling data through interaction with the environment, and optimizing a "surrogate" objective function using stochastic gradient ascent. Whereas standard policy gradient methods perform one gradient update per data sample, we propose a novel objective function that enables multiple epochs of minibatch updates. The new methods, which we call proximal policy optimization (PPO), have some of the benefits of trust region policy optimization (TRPO), but they are much simpler to implement, more general, and have better sample complexity (empirically). Our experiments test PPO on a collection of benchmark tasks, including simulated robotic locomotion and Atari game playing, and we show that PPO outperforms other online policy gradient methods, and overall strikes a favorable balance between sample complexity, simplicity, and wall-time.

While originally developed for continuous control problems, Proximal Policy Optimization (PPO) has emerged as the work-horse of a variety of reinforcement learning (RL) applications including the fine-tuning of generative models. Unfortunately, PPO requires multiple heuristics to enable stable convergence (e.g. value networks, clipping) and is notorious for its sensitivity to the precise implementation of these components. In response, we take a step back and ask what a minimalist RL algorithm for the era of generative models would look like. We propose REBEL, an algorithm that cleanly reduces the problem of policy optimization to regressing the relative rewards via a direct policy parameterization between two completions to a prompt, enabling strikingly lightweight implementation. In theory, we prove that fundamental RL algorithms like Natural Policy Gradient can be seen as variants of REBEL, which allows us to match the strongest known theoretical guarantees in terms of convergence and sample complexity in the RL literature. REBEL can also cleanly incorporate offline data and handle the intransitive preferences we frequently see in practice. Empirically, we find that REBEL provides a unified approach to language modeling and image generation with stronger or similar performance as PPO and DPO, all while being simpler to implement and more computationally tractable than PPO.

The rapid spread of multimodal misinformation on social media has raised growing concerns, while research on video misinformation detection remains limited due to the lack of large-scale, diverse datasets. Existing methods often overfit to rigid templates and lack deep reasoning over deceptive content. To address these challenges, we introduce FakeVV, a large-scale benchmark comprising over 100,000 video-text pairs with fine-grained, interpretable annotations. In addition, we further propose Fact-R1, a novel framework that integrates deep reasoning with collaborative rule-based reinforcement learning. Fact-R1 is trained through a three-stage process: (1) misinformation long-Chain-of-Thought (CoT) instruction tuning, (2) preference alignment via Direct Preference Optimization (DPO), and (3) Group Relative Policy Optimization (GRPO) using a novel verifiable reward function. This enables Fact-R1 to exhibit emergent reasoning behaviors comparable to those observed in advanced text-based reinforcement learning systems, but in the more complex multimodal misinformation setting. Our work establishes a new paradigm for misinformation detection, bridging large-scale video understanding, reasoning-guided alignment, and interpretable verification.

Reinforcement Learning, particularly through policy gradient methods, has played a central role in enabling reasoning capabilities of Large Language Models. However, the optimization stability of policy gradients in this setting remains understudied. As a result, existing implementations often resort to conservative hyperparameter choices to ensure stability, which requires more training samples and increases computational costs. Hence, developing models for reliably tracking the underlying optimization dynamics and leveraging them into training enables more sample-efficient regimes and further unleashes scalable post-training. We address this gap by formalizing the stochastic optimization problem of policy gradients with explicit consideration of second-order geometry. We propose a tractable computational framework that tracks and leverages curvature information during policy updates. We further employ this framework to design interventions in the optimization process through data selection. The resultant algorithm, Curvature-Aware Policy Optimization (CAPO), identifies samples that contribute to unstable updates and masks them out. Theoretically, we establish monotonic improvement guarantees under realistic assumptions. On standard math reasoning benchmarks, we empirically show that CAPO ensures stable updates under aggressive learning regimes where baselines catastrophically fail. With minimal intervention (rejecting fewer than 8% of tokens), CAPO achieves up to 30x improvement in sample efficiency over standard GRPO for LLM reasoning.

Recent advancements in Large Reasoning Models (LRMs), exemplified by DeepSeek-R1, have underscored the potential of scaling inference-time compute through Group Relative Policy Optimization (GRPO). However, GRPO frequently suffers from gradient signal attenuation when encountering problems that are either too trivial or overly complex. In these scenarios, the disappearance of inter-group advantages makes the gradient signal susceptible to noise, thereby jeopardizing convergence stability. While variants like DAPO attempt to rectify gradient vanishing, they do not alleviate the substantial computational overhead incurred by exhaustive rollouts on low-utility samples. In this paper, we propose Difficulty-Estimated Policy Optimization (DEPO), a novel framework designed to optimize the efficiency and robustness of reasoning alignment. DEPO integrates an online Difficulty Estimator that dynamically assesses and filters training data before the rollout phase. This mechanism ensures that computational resources are prioritized for samples with high learning potential. Empirical results demonstrate that DEPO achieves up to a 2x reduction in rollout costs without compromising model performance. Our approach significantly lowers the computational barrier for training high-performance reasoning models, offering a more sustainable path for reasoning scaling. Code and data will be released upon acceptance.

Ensuring factuality is essential for the safe use of Large Language Models (LLMs) in high-stakes domains such as medicine and law. Conformal inference provides distribution-free guarantees, but existing approaches are either overly conservative, discarding many true-claims, or rely on adaptive error rates and simple linear models that fail to capture complex group structures. To address these challenges, we reformulate conformal inference in a multiplicative filtering setting, modeling factuality as a product of claim-level scores. Our method, Multi-LLM Adaptive Conformal Inference (MACI), leverages ensembles to produce more accurate factuality-scores, which in our experiments led to higher retention, while validity is preserved through group-conditional calibration. Experiments show that MACI consistently achieves user-specified coverage with substantially higher retention and lower time cost than baselines. Our repository is available at https://github.com/MLAI-Yonsei/MACI

Large Language Models (LLMs) exhibit robust problem-solving capabilities for diverse tasks. However, most LLM-based agents are designed as specific task solvers with sophisticated prompt engineering, rather than agents capable of learning and evolving through interactions. These task solvers necessitate manually crafted prompts to inform task rules and regulate LLM behaviors, inherently incapacitating to address complex dynamic scenarios e.g., large interactive games. In light of this, we propose Agent-Pro: an LLM-based Agent with Policy-level Reflection and Optimization that can learn a wealth of expertise from interactive experiences and progressively elevate its behavioral policy. Specifically, it involves a dynamic belief generation and reflection process for policy evolution. Rather than action-level reflection, Agent-Pro iteratively reflects on past trajectories and beliefs, fine-tuning its irrational beliefs for a better policy. Moreover, a depth-first search is employed for policy optimization, ensuring continual enhancement in policy payoffs. Agent-Pro is evaluated across two games: Blackjack and Texas Hold'em, outperforming vanilla LLM and specialized models. Our results show Agent-Pro can learn and evolve in complex and dynamic scenes, which also benefits numerous LLM-based applications.

Reinforcement learning (RL) has emerged as a powerful tool for fine-tuning large language models (LLMs) to improve complex reasoning abilities. However, state-of-the-art policy optimization methods often suffer from high computational overhead and memory consumption, primarily due to the need for multiple generations per prompt and the reliance on critic networks or advantage estimates of the current policy. In this paper, we propose A*-PO, a novel two-stage policy optimization framework that directly approximates the optimal advantage function and enables efficient training of LLMs for reasoning tasks. In the first stage, we leverage offline sampling from a reference policy to estimate the optimal value function V*, eliminating the need for costly online value estimation. In the second stage, we perform on-policy updates using a simple least-squares regression loss with only a single generation per prompt. Theoretically, we establish performance guarantees and prove that the KL-regularized RL objective can be optimized without requiring complex exploration strategies. Empirically, A*-PO achieves competitive performance across a wide range of mathematical reasoning benchmarks, while reducing training time by up to 2times and peak memory usage by over 30% compared to PPO, GRPO, and REBEL. Implementation of A*-PO can be found at https://github.com/ZhaolinGao/A-PO.

Deceptive path planning (DPP) is the problem of designing a path that hides its true goal from an outside observer. Existing methods for DPP rely on unrealistic assumptions, such as global state observability and perfect model knowledge, and are typically problem-specific, meaning that even minor changes to a previously solved problem can force expensive computation of an entirely new solution. Given these drawbacks, such methods do not generalize to unseen problem instances, lack scalability to realistic problem sizes, and preclude both on-the-fly tunability of deception levels and real-time adaptivity to changing environments. In this paper, we propose a reinforcement learning (RL)-based scheme for training policies to perform DPP over arbitrary weighted graphs that overcomes these issues. The core of our approach is the introduction of a local perception model for the agent, a new state space representation distilling the key components of the DPP problem, the use of graph neural network-based policies to facilitate generalization and scaling, and the introduction of new deception bonuses that translate the deception objectives of classical methods to the RL setting. Through extensive experimentation we show that, without additional fine-tuning, at test time the resulting policies successfully generalize, scale, enjoy tunable levels of deception, and adapt in real-time to changes in the environment.

Group-based reinforcement learning (RL), such as GRPO, has advanced the capabilities of large language models on long-horizon agentic tasks. To enable more fine-grained policy updates, recent research has increasingly shifted toward stepwise group-based policy optimization, which treats each step in a rollout trajectory independently while using a memory module to retain historical context. However, we find a key issue in estimating stepwise relative advantages, namely context inconsistency, where steps within the same group may differ in their historical contexts. Empirically, we reveal that this issue can lead to severely biased advantage estimation, thereby degrading policy optimization significantly. To address the issue, in this paper, we propose Hierarchy-of-Groups Policy Optimization (HGPO) for long-horizon agentic tasks. Specifically, within a group of rollout trajectories, HGPO assigns each step to multiple hierarchical groups according to the consistency of historical contexts. Then, for each step, HGPO computes distinct advantages within each group and aggregates them with an adaptive weighting scheme. In this way, HGPO can achieve a favorable bias-variance trade-off in stepwise advantage estimation, without extra models or rollouts. Evaluations on two challenging agentic tasks, ALFWorld and WebShop with Qwen2.5-1.5B-Instruct and Qwen2.5-7B-Instruct, show that HGPO significantly outperforms existing agentic RL methods under the same computational constraints. Code is available at https://github.com/langfengQ/verl-agent/tree/master/recipe/hgpo.

Among on-policy reinforcement learning algorithms, Proximal Policy Optimization (PPO) demonstrates is widely favored for its simplicity, numerical stability, and strong empirical performance. Standard PPO relies on surrogate objectives defined via importance ratios, which require evaluating policy likelihood that is typically straightforward when the policy is modeled as a Gaussian distribution. However, extending PPO to more expressive, high-capacity policy models such as continuous normalizing flows (CNFs), also known as flow-matching models, is challenging because likelihood evaluation along the full flow trajectory is computationally expensive and often numerically unstable. To resolve this issue, we propose PolicyFlow, a novel on-policy CNF-based reinforcement learning algorithm that integrates expressive CNF policies with PPO-style objectives without requiring likelihood evaluation along the full flow path. PolicyFlow approximates importance ratios using velocity field variations along a simple interpolation path, reducing computational overhead without compromising training stability. To further prevent mode collapse and further encourage diverse behaviors, we propose the Brownian Regularizer, an implicit policy entropy regularizer inspired by Brownian motion, which is conceptually elegant and computationally lightweight. Experiments on diverse tasks across various environments including MultiGoal, PointMaze, IsaacLab and MuJoCo Playground show that PolicyFlow achieves competitive or superior performance compared to PPO using Gaussian policies and flow-based baselines including FPO and DPPO. Notably, results on MultiGoal highlight PolicyFlow's ability to capture richer multimodal action distributions.

The fluency and creativity of large pre-trained language models (LLMs) have led to their widespread use, sometimes even as a replacement for traditional search engines. Yet language models are prone to making convincing but factually inaccurate claims, often referred to as 'hallucinations.' These errors can inadvertently spread misinformation or harmfully perpetuate misconceptions. Further, manual fact-checking of model responses is a time-consuming process, making human factuality labels expensive to acquire. In this work, we fine-tune language models to be more factual, without human labeling and targeting more open-ended generation settings than past work. We leverage two key recent innovations in NLP to do so. First, several recent works have proposed methods for judging the factuality of open-ended text by measuring consistency with an external knowledge base or simply a large model's confidence scores. Second, the direct preference optimization algorithm enables straightforward fine-tuning of language models on objectives other than supervised imitation, using a preference ranking over possible model responses. We show that learning from automatically generated factuality preference rankings, generated either through existing retrieval systems or our novel retrieval-free approach, significantly improves the factuality (percent of generated claims that are correct) of Llama-2 on held-out topics compared with RLHF or decoding strategies targeted at factuality. At 7B scale, compared to Llama-2-chat, we observe 58% and 40% reduction in factual error rate when generating biographies and answering medical questions, respectively.

Behavior constrained policy optimization has been demonstrated to be a successful paradigm for tackling Offline Reinforcement Learning. By exploiting historical transitions, a policy is trained to maximize a learned value function while constrained by the behavior policy to avoid a significant distributional shift. In this paper, we propose our closed-form policy improvement operators. We make a novel observation that the behavior constraint naturally motivates the use of first-order Taylor approximation, leading to a linear approximation of the policy objective. Additionally, as practical datasets are usually collected by heterogeneous policies, we model the behavior policies as a Gaussian Mixture and overcome the induced optimization difficulties by leveraging the LogSumExp's lower bound and Jensen's Inequality, giving rise to a closed-form policy improvement operator. We instantiate offline RL algorithms with our novel policy improvement operators and empirically demonstrate their effectiveness over state-of-the-art algorithms on the standard D4RL benchmark. Our code is available at https://cfpi-icml23.github.io/.

Large language models (LLMs) exhibit hallucinations (i.e., unfaithful or nonsensical information) when serving as AI assistants in various domains. Since hallucinations always come with truthful content in the LLM responses, previous factuality alignment methods that conduct response-level preference learning inevitably introduced noises during training. Therefore, this paper proposes a fine-grained factuality alignment method based on Direct Preference Optimization (DPO), called Mask-DPO. Incorporating sentence-level factuality as mask signals, Mask-DPO only learns from factually correct sentences in the preferred samples and prevents the penalty on factual contents in the not preferred samples, which resolves the ambiguity in the preference learning. Extensive experimental results demonstrate that Mask-DPO can significantly improve the factuality of LLMs responses to questions from both in-domain and out-of-domain datasets, although these questions and their corresponding topics are unseen during training. Only trained on the ANAH train set, the score of Llama3.1-8B-Instruct on the ANAH test set is improved from 49.19% to 77.53%, even surpassing the score of Llama3.1-70B-Instruct (53.44%), while its FactScore on the out-of-domain Biography dataset is also improved from 30.29% to 39.39%. We further study the generalization property of Mask-DPO using different training sample scaling strategies and find that scaling the number of topics in the dataset is more effective than the number of questions. We provide a hypothesis of what factual alignment is doing with LLMs, on the implication of this phenomenon, and conduct proof-of-concept experiments to verify it. We hope the method and the findings pave the way for future research on scaling factuality alignment.

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.

As models increasingly leverage multi-step reasoning strategies to solve complex problems, supervising the logical validity of these intermediate steps has become a critical research challenge. Process reward models address this by providing step-by-step feedback, but current approaches have two major drawbacks: they typically function as classifiers without providing explanations, and their reliance on supervised fine-tuning with static datasets limits generalization. Inspired by recent advances, we reframe stepwise reward modeling from a classification task to a reasoning task itself. We thus propose a generative judge that reasons about the policy model's reasoning steps (i.e., meta-reasons), outputting thinking tokens before delivering a final verdict. Our model, StepWiser, is trained by reinforcement learning using relative outcomes of rollouts. We show it provides (i) better judgment accuracy on intermediate steps than existing methods; (ii) can be used to improve the policy model at training time; and (iii) improves inference-time search.

Chain-of-Thought (CoT) reasoning has significantly advanced the problem-solving capabilities of Large Language Models (LLMs), yet conventional CoT often exhibits internal determinism during decoding, limiting exploration of plausible alternatives. Recent methods attempt to address this by generating soft abstract tokens to enable reasoning in a continuous semantic space. However, we find that such approaches remain constrained by the greedy nature of autoregressive decoding, which fundamentally isolates the model from alternative reasoning possibilities. In this work, we propose Multi-Path Perception Policy Optimization (M3PO), a novel reinforcement learning framework that explicitly injects collective insights into the reasoning process. M3PO leverages parallel policy rollouts as naturally diverse reasoning sources and integrates cross-path interactions into policy updates through a lightweight collaborative mechanism. This design allows each trajectory to refine its reasoning with peer feedback, thereby cultivating more reliable multi-step reasoning patterns. Empirical results show that M3PO achieves state-of-the-art performance on both knowledge- and reasoning-intensive benchmarks. Models trained with M3PO maintain interpretability and inference efficiency, underscoring the promise of multi-path collaborative learning for robust reasoning.

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.

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.

We argue that inventory management presents unique opportunities for the reliable application of deep reinforcement learning (DRL). To enable this, we emphasize and test two complementary techniques. The first is Hindsight Differentiable Policy Optimization (HDPO), which uses pathwise gradients from offline counterfactual simulations to directly and efficiently optimize policy performance. Unlike standard policy gradient methods that rely on high-variance score-function estimators, HDPO computes gradients by differentiating through the known system dynamics. Via extensive benchmarking, we show that HDPO recovers near-optimal policies in settings with known or bounded optima, is more robust than variants of the REINFORCE algorithm, and significantly outperforms generalized newsvendor heuristics on problems using real time series data. Our second technique aligns neural policy architectures with the topology of the inventory network. We exploit Graph Neural Networks (GNNs) as a natural inductive bias for encoding supply chain structure, demonstrate that they can represent optimal and near-optimal policies in two theoretical settings, and empirically show that they reduce data requirements across six diverse inventory problems. A key obstacle to progress in this area is the lack of standardized benchmark problems. To address this gap, we open-source a suite of benchmark environments, along with our full codebase, to promote transparency and reproducibility. All resources are available at github.com/MatiasAlvo/Neural_inventory_control.

Reasoning Large Language Models (R-LLMs) have significantly advanced complex reasoning tasks but often struggle with factuality, generating substantially more hallucinations than their non-reasoning counterparts on long-form factuality benchmarks. However, extending online Reinforcement Learning (RL), a key component in recent R-LLM advancements, to the long-form factuality setting poses several unique challenges due to the lack of reliable verification methods. Previous work has utilized automatic factuality evaluation frameworks such as FActScore to curate preference data in the offline RL setting, yet we find that directly leveraging such methods as the reward in online RL leads to reward hacking in multiple ways, such as producing less detailed or relevant responses. We propose a novel reward function that simultaneously considers the factual precision, response detail level, and answer relevance, and applies online RL to learn high quality factual reasoning. Evaluated on six long-form factuality benchmarks, our factual reasoning model achieves an average reduction of 23.1 percentage points in hallucination rate, a 23% increase in answer detail level, and no degradation in the overall response helpfulness.

Reinforcement Learning with Verifiable Rewards (RLVR) has become a central post-training paradigm for improving the reasoning capabilities of large language models. Yet existing methods share a common blind spot: they optimize policies based on instantaneous group-level or batch-level statistics without ever verifying whether the resulting update actually improved the model. This open-loop design -- updating in isolation at each step, guided only by within-group (batch) reward signals -- means optimization can drift or collapse with no mechanism to detect and correct these failures. We argue that the missing ingredient is policy improvement feedback: the ability to measure and optimize inter-iteration progress directly. To this end, we introduce Policy Improvement Reinforcement Learning (PIRL), a framework that replaces surrogate reward maximization with the explicit objective of maximizing cumulative policy improvement across iterations, and prove this temporal objective is perfectly aligned with maximizing final task performance. Building on PIRL, we propose Policy Improvement Policy Optimization (PIPO), which implements closed-loop optimization through retrospective verification. At each iteration, PIPO evaluates whether the previous update yielded genuine improvement against a sliding-window historical baseline, then actively reinforces beneficial updates and suppresses the harmful ones -- transforming an open-loop process into a self-correcting one. We provide theoretical analysis showing that PIPO performs ascent on the PIRL objective in expectation, and experiments on mathematical reasoning benchmarks demonstrate improved stability and performance over GRPO and its variants.

RL-based agentic search enables LLMs to solve complex questions via dynamic planning and external search. While this approach significantly enhances accuracy with agent policies optimized via large-scale reinforcement learning, we identify a critical gap in reliability: these agents fail to recognize their reasoning boundaries and rarely admit ``I DON'T KNOW'' (IDK) even when evidence is insufficient or reasoning reaches its limit. The lack of reliability often leads to plausible but unreliable answers, introducing significant risks in many real-world scenarios. To this end, we propose Boundary-Aware Policy Optimization (BAPO), a novel RL framework designed to cultivate reliable boundary awareness without compromising accuracy. BAPO introduces two key components: (i) a group-based boundary-aware reward that encourages an IDK response only when the reasoning reaches its limit, and (ii) an adaptive reward modulator that strategically suspends this reward during early exploration, preventing the model from exploiting IDK as a shortcut. Extensive experiments on four benchmarks demonstrate that BAPO substantially enhances the overall reliability of agentic search.

Tool-integrated reasoning (TIR) enables LLM agents to solve tasks through planning, tool use, and iterative revision, but outcome-only reinforcement learning in this setting suffers from sparse, delayed rewards and weak step-level credit assignment. In long-horizon TIR trajectories, an early irrecoverable mistake can determine success or failure, making it crucial to localize the first irrecoverable step and leverage it for fine-grained credit assignment. We propose Error-Localized Policy Optimization (ELPO), which localizes the first irrecoverable step via binary-search rollout trees under a fixed rollout budget, converts the resulting tree into stable learning signals through hierarchical advantage attribution, and applies error-localized adaptive clipping to strengthen corrective updates on the critical step and its suffix. Across TIR benchmarks in math, science QA, and code execution, ELPO consistently outperforms strong Agentic RL baselines under comparable sampling budgets, with additional gains in Pass@K and Major@K scaling, rollout ranking quality, and tool-call efficiency. Our code will be publicly released soon.

In recent years, various powerful policy gradient algorithms have been proposed in deep reinforcement learning. While all these algorithms build on the Policy Gradient Theorem, the specific design choices differ significantly across algorithms. We provide a holistic overview of on-policy policy gradient algorithms to facilitate the understanding of both their theoretical foundations and their practical implementations. In this overview, we include a detailed proof of the continuous version of the Policy Gradient Theorem, convergence results and a comprehensive discussion of practical algorithms. We compare the most prominent algorithms on continuous control environments and provide insights on the benefits of regularization. All code is available at https://github.com/Matt00n/PolicyGradientsJax.

Direct Preference Optimization (DPO) using an implicit reward model has proven to be an effective alternative to reinforcement learning from human feedback (RLHF) for fine-tuning preference aligned large language models (LLMs). However, the overall preference annotations of responses do not fully capture the fine-grained quality of model outputs in complex multi-step reasoning tasks, such as mathematical reasoning. To address this limitation, we introduce a novel algorithm called Step-level Value Preference Optimization (SVPO). Our approach employs Monte Carlo Tree Search (MCTS) to automatically annotate step-level preferences for multi-step reasoning. Furthermore, from the perspective of learning-to-rank, we train an explicit value model to replicate the behavior of the implicit reward model, complementing standard preference optimization. This value model enables the LLM to generate higher reward responses with minimal cost during inference. Experimental results demonstrate that our method achieves state-of-the-art performance on both in-domain and out-of-domain mathematical reasoning benchmarks. Our code is available at https://github.com/MARIO-Math-Reasoning/Super_MARIO.

Hallucination and factuality deficits remain key obstacles to the reliability of large language models (LLMs) in long-form generation. Existing reinforcement learning from human feedback (RLHF) frameworks primarily rely on preference rewards, yet they often overlook the model's internal knowledge boundaries, exacerbating the so-called "hallucination tax". To address this challenge, we propose Knowledge-Level Consistency Reinforcement Learning Framework (KLCF), a novel framework that focuses on the knowledge consistency between the policy model's expressed knowledge and the base model's parametric knowledge, and introduces a Dual-Fact Alignment mechanism to jointly optimize factual recall and precision. Specifically, KLCF leverages pretrained knowledge boundaries to construct fact checklist, guiding online reinforcement learning to improve factual coverage and recall; simultaneously, it trains a self-assessment module based on the base model's internal knowledge to enhance factual precision during generation. Unlike prior methods that rely on external retrieval or heavy verification, our reward design is fully external-knowledge-free and lightweight, making KLCF efficient and easily scalable to large-scale training. Experimental results demonstrate that KLCF substantially improves factuality metrics across multiple long-form benchmarks and effectively alleviates model hallucinations.

The outstanding capabilities of large language models (LLMs) render them a crucial component in various autonomous agent systems. While traditional methods depend on the inherent knowledge of LLMs without fine-tuning, more recent approaches have shifted toward the reinforcement learning strategy to further enhance agents' ability to solve complex interactive tasks with environments and tools. However, previous approaches are constrained by the sparse reward issue, where existing datasets solely provide a final scalar reward for each multi-step reasoning chain, potentially leading to ineffectiveness and inefficiency in policy learning. In this paper, we introduce StepAgent, which utilizes step-wise reward to optimize the agent's reinforcement learning process. Inheriting the spirit of novice-to-expert theory, we first compare the actions of the expert and the agent to automatically generate intermediate rewards for fine-grained optimization. Additionally, we propose implicit-reward and inverse reinforcement learning techniques to facilitate agent reflection and policy adjustment. Further theoretical analysis demonstrates that the action distribution of the agent can converge toward the expert action distribution over multiple training cycles. Experimental results across various datasets indicate that StepAgent outperforms existing baseline methods.

We focus on developing efficient and reliable policy optimization strategies for robot learning with real-world data. In recent years, policy gradient methods have emerged as a promising paradigm for training control policies in simulation. However, these approaches often remain too data inefficient or unreliable to train on real robotic hardware. In this paper we introduce a novel policy gradient-based policy optimization framework which systematically leverages a (possibly highly simplified) first-principles model and enables learning precise control policies with limited amounts of real-world data. Our approach 1) uses the derivatives of the model to produce sample-efficient estimates of the policy gradient and 2) uses the model to design a low-level tracking controller, which is embedded in the policy class. Theoretical analysis provides insight into how the presence of this feedback controller addresses overcomes key limitations of stand-alone policy gradient methods, while hardware experiments with a small car and quadruped demonstrate that our approach can learn precise control strategies reliably and with only minutes of real-world data.

Flow-based vision-language-action (VLA) models excel in embodied control but suffer from intractable likelihoods during multi-step sampling, hindering online reinforcement learning. We propose \textit{boldsymbolπ-StepNFT} (Step-wise Negative-aware Fine-Tuning), a critic-and-likelihood-free framework that requires only a single forward pass per optimization step and eliminates auxiliary value networks. We identify that wider exploration spaces necessitate finer-grained, step-wise guidance for alignment. Empirically, π-StepNFT unlocks latent potential on LIBERO with competitive few-shot robustness. Moreover, it achieves superior generalization on ManiSkill, outperforming value-based baselines in OOD scenarios by preventing overfitting to multimodal features. This property offers a scalable solution promising for complex real-world applications.

Test-time scaling has proven effective in further enhancing the performance of pretrained Large Language Models (LLMs). However, mainstream post-training methods (i.e., reinforcement learning (RL) with chain-of-thought (CoT) reasoning) often incur substantial computational overhead due to auxiliary models and overthinking. In this paper, we empirically reveal that the incorrect answers partially stem from verbose reasoning processes lacking correct self-fix, where errors accumulate across multiple reasoning steps. To this end, we propose Self-traced Step-wise Preference Optimization (SSPO), a pluggable RL process supervision framework that enables fine-grained optimization of each reasoning step. Specifically, SSPO requires neither auxiliary models nor stepwise manual annotations. Instead, it leverages step-wise preference signals generated by the model itself to guide the optimization process for reasoning compression. Experiments demonstrate that the generated reasoning sequences from SSPO are both accurate and succinct, effectively mitigating overthinking behaviors without compromising model performance across diverse domains and languages.

Recently, the impressive empirical success of policy gradient (PG) methods has catalyzed the development of their theoretical foundations. Despite the huge efforts directed at the design of efficient stochastic PG-type algorithms, the understanding of their convergence to a globally optimal policy is still limited. In this work, we develop improved global convergence guarantees for a general class of Fisher-non-degenerate parameterized policies which allows to address the case of continuous state action spaces. First, we propose a Normalized Policy Gradient method with Implicit Gradient Transport (N-PG-IGT) and derive a mathcal{O}(varepsilon^{-2.5}) sample complexity of this method for finding a global varepsilon-optimal policy. Improving over the previously known mathcal{O}(varepsilon^{-3}) complexity, this algorithm does not require the use of importance sampling or second-order information and samples only one trajectory per iteration. Second, we further improve this complexity to mathcal{mathcal{O} }(varepsilon^{-2}) by considering a Hessian-Aided Recursive Policy Gradient ((N)-HARPG) algorithm enhanced with a correction based on a Hessian-vector product. Interestingly, both algorithms are (i) simple and easy to implement: single-loop, do not require large batches of trajectories and sample at most two trajectories per iteration; (ii) computationally and memory efficient: they do not require expensive subroutines at each iteration and can be implemented with memory linear in the dimension of parameters.

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.

While Reinforcement Learning (RL) has advanced LLM reasoning, applying it to long-context scenarios is hindered by sparsity of outcome rewards. This limitation fails to penalize ungrounded "lucky guesses," leaving the critical process of needle-in-a-haystack evidence retrieval largely unsupervised. To address this, we propose EAPO (Evidence-Augmented Policy Optimization). We first establish the Evidence-Augmented Reasoning paradigm, validating via Tree-Structured Evidence Sampling that precise evidence extraction is the decisive bottleneck for long-context reasoning. Guided by this insight, EAPO introduces a specialized RL algorithm where a reward model computes a Group-Relative Evidence Reward, providing dense process supervision to explicitly improve evidence quality. To sustain accurate supervision throughout training, we further incorporate an Adaptive Reward-Policy Co-Evolution mechanism. This mechanism iteratively refines the reward model using outcome-consistent rollouts, sharpening its discriminative capability to ensure precise process guidance. Comprehensive evaluations across eight benchmarks demonstrate that EAPO significantly enhances long-context reasoning performance compared to SOTA baselines.

We introduce Diffusion Policy Policy Optimization, DPPO, an algorithmic framework including best practices for fine-tuning diffusion-based policies (e.g. Diffusion Policy) in continuous control and robot learning tasks using the policy gradient (PG) method from reinforcement learning (RL). PG methods are ubiquitous in training RL policies with other policy parameterizations; nevertheless, they had been conjectured to be less efficient for diffusion-based policies. Surprisingly, we show that DPPO achieves the strongest overall performance and efficiency for fine-tuning in common benchmarks compared to other RL methods for diffusion-based policies and also compared to PG fine-tuning of other policy parameterizations. Through experimental investigation, we find that DPPO takes advantage of unique synergies between RL fine-tuning and the diffusion parameterization, leading to structured and on-manifold exploration, stable training, and strong policy robustness. We further demonstrate the strengths of DPPO in a range of realistic settings, including simulated robotic tasks with pixel observations, and via zero-shot deployment of simulation-trained policies on robot hardware in a long-horizon, multi-stage manipulation task. Website with code: diffusion-ppo.github.io

Direct Preference Optimization (DPO) often struggles with long-chain mathematical reasoning. Existing approaches, such as Step-DPO, typically improve this by focusing on the first erroneous step in the reasoning chain. However, they overlook all other steps and rely heavily on humans or GPT-4 to identify erroneous steps. To address these issues, we propose Full-Step-DPO, a novel DPO framework tailored for mathematical reasoning. Instead of optimizing only the first erroneous step, it leverages step-wise rewards from the entire reasoning chain. This is achieved by training a self-supervised process reward model, which automatically scores each step, providing rewards while avoiding reliance on external signals. Furthermore, we introduce a novel step-wise DPO loss, which dynamically updates gradients based on these step-wise rewards. This endows stronger reasoning capabilities to language models. Extensive evaluations on both in-domain and out-of-domain mathematical reasoning benchmarks across various base language models, demonstrate that Full-Step-DPO achieves superior performance compared to state-of-the-art baselines.

Large Language Models (LLMs) using Chain-of-Thought (CoT) prompting excel at complex reasoning but generate verbose thought processes with considerable redundancy, leading to increased inference costs and reduced efficiency. We introduce a novel CoT compression framework based on step entropy, a metric that quantifies the informational contribution of individual reasoning steps to identify redundancy. Through theoretical analysis and extensive empirical validation on mathematical reasoning benchmarks, we demonstrate that steps with low entropy are indeed highly redundant. Our experiments reveal that an astonishing 80\% of low-entropy intermediate steps can be pruned with minor degradation in the final answer accuracy across DeepSeek-R1-7B, 14B and Qwen3-8B. This finding sharply contrasts with random or high-entropy pruning, which severely impairs reasoning performance. Building on this, we propose a novel two-stage training strategy combining Supervised Fine-Tuning (SFT) and Group Relative Policy Optimization (GRPO) reinforcement learning. This approach enables LLMs to autonomously learn to generate compressed COTs during inference by strategically incorporating [SKIP] tokens. Our method significantly enhances LLM inference efficiency while rigorously preserving accuracy, offering profound implications for practical LLM deployment and a deeper understanding of reasoning structures.

Reinforcement learning (RL) has become a cornerstone for fine-tuning Large Language Models (LLMs), with Proximal Policy Optimization (PPO) serving as the de facto standard algorithm. Despite its ubiquity, we argue that the core ratio clipping mechanism in PPO is structurally ill-suited for the large vocabularies inherent to LLMs. PPO constrains policy updates based on the probability ratio of sampled tokens, which serves as a noisy single-sample Monte Carlo estimate of the true policy divergence. This creates a sub-optimal learning dynamic: updates to low-probability tokens are aggressively over-penalized, while potentially catastrophic shifts in high-probability tokens are under-constrained, leading to training inefficiency and instability. To address this, we propose Divergence Proximal Policy Optimization (DPPO), which substitutes heuristic clipping with a more principled constraint based on a direct estimate of policy divergence (e.g., Total Variation or KL). To avoid huge memory footprint, we introduce the efficient Binary and Top-K approximations to capture the essential divergence with negligible overhead. Extensive empirical evaluations demonstrate that DPPO achieves superior training stability and efficiency compared to existing methods, offering a more robust foundation for RL-based LLM fine-tuning.

Large reasoning models (LRMs) show strong capabilities in complex reasoning, yet their marginal gains on evidence-dependent factual questions are limited. We find this limitation is partially attributable to a reasoning-answer hit gap, where the model identifies the correct facts during reasoning but fails to incorporate them into the final response, thereby reducing factual fidelity. To address this issue, we propose MR-ALIGN, a Meta-Reasoning informed alignment framework that enhances factuality without relying on external verifiers. MR-ALIGN quantifies state transition probabilities along the model's thinking process and constructs a transition-aware implicit reward that reinforces beneficial reasoning patterns while suppressing defective ones at the atomic thinking segments. This re-weighting reshapes token-level signals into probability-aware segment scores, encouraging coherent reasoning trajectories that are more conducive to factual correctness. Empirical evaluations across four factual QA datasets and one long-form factuality benchmark show that MR-ALIGN consistently improves accuracy and truthfulness while reducing misleading reasoning. These results highlight that aligning the reasoning process itself, rather than merely the outputs, is pivotal for advancing factuality in LRMs.

Mathematical reasoning presents a significant challenge for Large Language Models (LLMs) due to the extensive and precise chain of reasoning required for accuracy. Ensuring the correctness of each reasoning step is critical. To address this, we aim to enhance the robustness and factuality of LLMs by learning from human feedback. However, Direct Preference Optimization (DPO) has shown limited benefits for long-chain mathematical reasoning, as models employing DPO struggle to identify detailed errors in incorrect answers. This limitation stems from a lack of fine-grained process supervision. We propose a simple, effective, and data-efficient method called Step-DPO, which treats individual reasoning steps as units for preference optimization rather than evaluating answers holistically. Additionally, we have developed a data construction pipeline for Step-DPO, enabling the creation of a high-quality dataset containing 10K step-wise preference pairs. We also observe that in DPO, self-generated data is more effective than data generated by humans or GPT-4, due to the latter's out-of-distribution nature. Our findings demonstrate that as few as 10K preference data pairs and fewer than 500 Step-DPO training steps can yield a nearly 3% gain in accuracy on MATH for models with over 70B parameters. Notably, Step-DPO, when applied to Qwen2-72B-Instruct, achieves scores of 70.8% and 94.0% on the test sets of MATH and GSM8K, respectively, surpassing a series of closed-source models, including GPT-4-1106, Claude-3-Opus, and Gemini-1.5-Pro. Our code, data, and models are available at https://github.com/dvlab-research/Step-DPO.

We introduce an approach aimed at enhancing the reasoning capabilities of Large Language Models (LLMs) through an iterative preference learning process inspired by the successful strategy employed by AlphaZero. Our work leverages Monte Carlo Tree Search (MCTS) to iteratively collect preference data, utilizing its look-ahead ability to break down instance-level rewards into more granular step-level signals. To enhance consistency in intermediate steps, we combine outcome validation and stepwise self-evaluation, continually updating the quality assessment of newly generated data. The proposed algorithm employs Direct Preference Optimization (DPO) to update the LLM policy using this newly generated step-level preference data. Theoretical analysis reveals the importance of using on-policy sampled data for successful self-improving. Extensive evaluations on various arithmetic and commonsense reasoning tasks demonstrate remarkable performance improvements over existing models. For instance, our approach outperforms the Mistral-7B Supervised Fine-Tuning (SFT) baseline on GSM8K, MATH, and ARC-C, with substantial increases in accuracy to 81.8% (+5.9%), 34.7% (+5.8%), and 76.4% (+15.8%), respectively. Additionally, our research delves into the training and inference compute tradeoff, providing insights into how our method effectively maximizes performance gains. Our code is publicly available at https://github.com/YuxiXie/MCTS-DPO.

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 Reinforcement Learning with Verifiable Rewards (RLVR) for Large Language Model (LLM) reasoning have been hindered by a persistent challenge: exploration collapse. The semantic homogeneity of random rollouts often traps models in narrow, over-optimized behaviors. While existing methods leverage policy entropy to encourage exploration, they face inherent limitations. Global entropy regularization is susceptible to reward hacking, which can induce meaningless verbosity, whereas local token-selective updates struggle with the strong inductive bias of pre-trained models. To address this, we propose Latent Policy Optimization via Iterative Information Bottleneck (IIB-LPO), a novel approach that shifts exploration from statistical perturbation of token distributions to topological branching of reasoning trajectories. IIB-LPO triggers latent branching at high-entropy states to diversify reasoning paths and employs the Information Bottleneck principle both as a trajectory filter and a self-reward mechanism, ensuring concise and informative exploration. Empirical results across four mathematical reasoning benchmarks demonstrate that IIB-LPO achieves state-of-the-art performance, surpassing prior methods by margins of up to 5.3% in accuracy and 7.4% in diversity metrics.

Reinforcement Learning with Verifiable Rewards (RLVR) has achieved remarkable success in improving autoregressive models, especially in domains requiring correctness like mathematical reasoning and code generation. However, directly applying such paradigms to Diffusion Large Language Models (dLLMs) is fundamentally hindered by the intractability of exact likelihood computation, which forces existing methods to rely on high-variance approximations. To bridge this gap, we propose Likelihood-Free Policy Optimization (LFPO), a native framework that maps the concept of vector field flow matching to the discrete token space. Specifically, LFPO formulates alignment as geometric velocity rectification, which directly optimizes denoising logits via contrastive updates. This design effectively bypasses the errors inherent in likelihood approximation, yielding the precise gradient estimation. Furthermore, LFPO enforce consistency by predicting final solutions from intermediate steps, effectively straightening the probability flow to enable high-quality generation with significantly fewer iterations. Extensive experiments demonstrate that LFPO not only outperforms state-of-the-art baselines on code and reasoning benchmarks but also accelerates inference by approximately 20% through reduced diffusion steps.

Generative models, like flows and diffusions, have recently emerged as popular and efficacious policy parameterizations in robotics. There has been much speculation as to the factors underlying their successes, ranging from capturing multi-modal action distribution to expressing more complex behaviors. In this work, we perform a comprehensive evaluation of popular generative control policies (GCPs) on common behavior cloning (BC) benchmarks. We find that GCPs do not owe their success to their ability to capture multi-modality or to express more complex observation-to-action mappings. Instead, we find that their advantage stems from iterative computation, as long as intermediate steps are supervised during training and this supervision is paired with a suitable level of stochasticity. As a validation of our findings, we show that a minimum iterative policy (MIP), a lightweight two-step regression-based policy, essentially matches the performance of flow GCPs, and often outperforms distilled shortcut models. Our results suggest that the distribution-fitting component of GCPs is less salient than commonly believed, and point toward new design spaces focusing solely on control performance. Project page: https://simchowitzlabpublic.github.io/much-ado-about-noising-project/

Large Language Models (LLMs) have demonstrated remarkable capabilities but often face challenges with tasks requiring sophisticated reasoning. While Chain-of-Thought (CoT) prompting significantly enhances reasoning, it indiscriminately generates lengthy reasoning steps for all queries, leading to substantial computational costs and inefficiency, especially for simpler inputs. To address this critical issue, we introduce AdaCoT (Adaptive Chain-of-Thought), a novel framework enabling LLMs to adaptively decide when to invoke CoT. AdaCoT framed adaptive reasoning as a Pareto optimization problem that seeks to balance model performance with the costs associated with CoT invocation (both frequency and computational overhead). We propose a reinforcement learning (RL) based method, specifically utilizing Proximal Policy Optimization (PPO), to dynamically control the CoT triggering decision boundary by adjusting penalty coefficients, thereby allowing the model to determine CoT necessity based on implicit query complexity. A key technical contribution is Selective Loss Masking (SLM), designed to counteract decision boundary collapse during multi-stage RL training, ensuring robust and stable adaptive triggering. Experimental results demonstrate that AdaCoT successfully navigates the Pareto frontier, achieving substantial reductions in CoT usage for queries not requiring elaborate reasoning. For instance, on our production traffic testset, AdaCoT reduced CoT triggering rates to as low as 3.18\% and decreased average response tokens by 69.06%, while maintaining high performance on complex tasks.

Reinforcement learning with verifiable rewards (RLVR) has become a standard approach for large language models (LLMs) post-training to incentivize reasoning capacity. Among existing recipes, group-based policy gradient is prevalent, which samples a group of responses per prompt and updates the policy via group-relative advantage signals. This work reveals that these optimization strategies share a common geometric structure: each implicitly defines a target distribution on the response simplex and projects toward it via first-order approximation. Building on this insight, we propose Listwise Policy Optimization (LPO) to explicitly conduct the target-projection, which demystifies the implicit target by restricting the proximal RL objective to the response simplex, and then projects the policy via exact divergence minimization. This framework provides (i) monotonic improvement on the listwise objective with bounded, zero-sum, and self-correcting projection gradients, and (ii) flexibility in divergence selection with distinct structural properties through the decoupled projection step. On diverse reasoning tasks and LLM backbones, LPO consistently improves training performance over typical policy gradient baselines under matched targets, while intrinsically preserving optimization stability and response diversity.

Current research on the Decompose-Then-Verify paradigm for evaluating the factuality of long-form text typically treats decomposition and verification in isolation, overlooking their interactions and potential misalignment. We find that existing decomposition policies, typically hand-crafted demonstrations, do not align well with downstream verifiers in terms of atomicity -- a novel metric quantifying information density -- leading to suboptimal verification results. We formulate finding the optimal decomposition policy for optimal verification as a bilevel optimization problem. To approximate a solution for this strongly NP-hard problem, we propose dynamic decomposition, a reinforcement learning framework that leverages verifier feedback to learn a policy for dynamically decomposing claims to verifier-preferred atomicity. Experimental results show that dynamic decomposition outperforms existing decomposition policies, improving verification confidence by 0.07 and accuracy by 0.12 (on a 0-1 scale) on average across varying verifiers, datasets, and atomcities of input claims.

Reinforcement learning with verifiable rewards (RLVR) for Large Reasoning Models hinges on baseline estimation for variance reduction, but existing approaches pay a heavy price: PPO requires a policy-model scale critic, while GRPO needs multiple rollouts per prompt to keep its empirical group mean stable. We introduce Policy Optimization with Internal State Value Estimation), which obtains a baseline at negligible cost by using the policy model's internal signals already computed during the policy forward pass. A lightweight probe predicts the expected verifiable reward from the hidden states of the prompt and generated trajectory, as well as token-entropy statistics, and is trained online alongside the policy. To preserve gradient unbiasedness despite using trajectory-conditioned features, we introduce a cross-rollout construction that predicts each rollout's value from an independent rollout's internal states. Because POISE estimates prompt value using only a single rollout, it enables higher prompt diversity for a fixed compute budget during training. This reduces gradient variance for more stable learning and also eliminates the compute overhead of sampling costs for detecting zero-advantage prompts. On Qwen3-4B and DeepSeek-R1-Distill-Qwen-1.5B across math reasoning benchmarks, POISE matches DAPO while requiring less compute. Moreover, its value estimator shows similar performance to a separate LLM-scale value model and generalizes to various verifiable tasks. By leveraging the model's own internal representations, POISE enables more stable and efficient policy optimization.

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.

Reinforcement learning has been central to recent advances in large language model reasoning, but most algorithms rely on on-policy training that demands fresh rollouts at every update, limiting efficiency and scalability. Asynchronous RL systems alleviate this by decoupling rollout generation from training, yet their effectiveness hinges on tolerating large staleness in rollout data, a setting where existing methods either degrade in performance or collapse. We revisit this challenge and uncover a prosperity-before-collapse phenomenon: stale data can be as informative as on-policy data if exploited properly. Building on this insight, we introduce M2PO (Second-Moment Trust Policy Optimization), which constrains the second moment of importance weights to suppress only extreme outliers while preserving informative updates. Notably, M2PO sharply reduces the fraction of clipped tokens under high staleness (from 1.22% to 0.06% over training), precisely masking high-variance tokens while maintaining stable optimization. Extensive evaluation across six models (from 1.7B to 32B) and eight benchmarks shows that M2PO delivers stable off-policy training even with data stale by at least 256 model updates and matches on-policy performance.

Recent improvements in conditional generative modeling have made it possible to generate high-quality images from language descriptions alone. We investigate whether these methods can directly address the problem of sequential decision-making. We view decision-making not through the lens of reinforcement learning (RL), but rather through conditional generative modeling. To our surprise, we find that our formulation leads to policies that can outperform existing offline RL approaches across standard benchmarks. By modeling a policy as a return-conditional diffusion model, we illustrate how we may circumvent the need for dynamic programming and subsequently eliminate many of the complexities that come with traditional offline RL. We further demonstrate the advantages of modeling policies as conditional diffusion models by considering two other conditioning variables: constraints and skills. Conditioning on a single constraint or skill during training leads to behaviors at test-time that can satisfy several constraints together or demonstrate a composition of skills. Our results illustrate that conditional generative modeling is a powerful tool for decision-making.

The role of reinforcement learning (RL) in enhancing the reasoning of large language models (LLMs) is becoming increasingly significant. Despite the success of RL in many scenarios, there are still many challenges in improving the reasoning of LLMs. One challenge is the sparse reward, which makes optimization difficult for RL and necessitates a large amount of data samples. Another challenge stems from the inherent instability of RL, particularly when using Actor-Critic (AC) methods to derive optimal policies, which often leads to unstable training processes. To address these issues, we introduce Direct Advantage Policy Optimization (DAPO), an novel step-level offline RL algorithm. Unlike standard alignment that rely solely outcome rewards to optimize policies (such as DPO), DAPO employs a critic function to predict the reasoning accuracy at each step, thereby generating dense signals to refine the generation strategy. Additionally, the Actor and Critic components in DAPO are trained independently, avoiding the co-training instability observed in standard AC algorithms like PPO. We train DAPO on mathematical and code query datasets and then evaluate its performance on multiple benchmarks. Our results show that DAPO can effectively enhance the mathematical and code capabilities on both SFT models and RL models, demonstrating the effectiveness of DAPO.

Policy gradient is a widely utilized and foundational algorithm in the field of reinforcement learning (RL). Renowned for its convergence guarantees and stability compared to other RL algorithms, its practical application is often hindered by sensitivity to hyper-parameters, particularly the step-size. In this paper, we introduce the integration of the Polyak step-size in RL, which automatically adjusts the step-size without prior knowledge. To adapt this method to RL settings, we address several issues, including unknown f* in the Polyak step-size. Additionally, we showcase the performance of the Polyak step-size in RL through experiments, demonstrating faster convergence and the attainment of more stable policies.

Reinforcement Learning (RL) has demonstrated tremendous empirical success across numerous challenging domains. However, we lack a strong theoretical understanding of the statistical complexity of RL in environments with large state spaces, where function approximation is required for sample-efficient learning. This thesis addresses this gap by rigorously examining the statistical complexity of RL with function approximation from a learning theoretic perspective. Departing from a long history of prior work, we consider the weakest form of function approximation, called agnostic policy learning, in which the learner seeks to find the best policy in a given class Pi, with no guarantee that Pi contains an optimal policy for the underlying task. We systematically explore agnostic policy learning along three key axes: environment access -- how a learner collects data from the environment; coverage conditions -- intrinsic properties of the underlying MDP measuring the expansiveness of state-occupancy measures for policies in the class Pi, and representational conditions -- structural assumptions on the class Pi itself. Within this comprehensive framework, we (1) design new learning algorithms with theoretical guarantees and (2) characterize fundamental performance bounds of any algorithm. Our results reveal significant statistical separations that highlight the power and limitations of agnostic policy learning.

Misinformation and disinformation demand fact checking that goes beyond simple evidence-based reasoning. Existing benchmarks fall short: they are largely single modality (text-only), span short time horizons, use shallow evidence, cover domains unevenly, and often omit full articles -- obscuring models' real-world capability. We present MMM-Fact, a large-scale benchmark of 125,449 fact-checked statements (1995--2025) across multiple domains, each paired with the full fact-check article and multimodal evidence (text, images, videos, tables) from four fact-checking sites and one news outlet. To reflect verification effort, each statement is tagged with a retrieval-difficulty tier -- Basic (1--5 sources), Intermediate (6--10), and Advanced (>10) -- supporting fairness-aware evaluation for multi-step, cross-modal reasoning. The dataset adopts a three-class veracity scheme (true/false/not enough information) and enables tasks in veracity prediction, explainable fact-checking, complex evidence aggregation, and longitudinal analysis. Baselines with mainstream LLMs show MMM-Fact is markedly harder than prior resources, with performance degrading as evidence complexity rises. MMM-Fact offers a realistic, scalable benchmark for transparent, reliable, multimodal fact-checking.

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.

Reinforcement learning is a framework for learning to act sequentially in an unknown environment. We propose a natural approach for modeling policy structure in policy gradients. The key idea is to optimize for a subset of future rewards: smaller subsets represent simpler policies, which can be learned more reliably because their empirical gradient estimates are more accurate. Our approach allows for modeling and comparison of different policy classes, including full planning, greedy, K-step lookahead, and segment policies. We evaluate the policies empirically on multiple persona-alignment conversational problems. Different policies excel in different problems, reflecting their different characteristics and highlighting the importance of our studied policy class.

In the field of online reinforcement learning (RL), traditional Gaussian policies and flow-based methods are often constrained by their unimodal expressiveness, complex gradient clipping, or stringent trust-region requirements. Moreover, they all rely on post-hoc penalization of negative samples to correct erroneous actions. This paper introduces Positive-Only Drifting Policy Optimization (PODPO), a likelihood-free and gradient-clipping-free generative approach for online RL. By leveraging the drifting model, PODPO performs policy updates via advantage-weighted local contrastive drifting. Relying solely on positive-advantage samples, it elegantly steers actions toward high-return regions while exploiting the inherent local smoothness of the generative model to enable proactive error prevention. In doing so, PODPO opens a promising new pathway for generative policy learning in online settings.

Aligning large language models (LLMs) on domain-specific data remains a fundamental challenge. Supervised fine-tuning (SFT) offers a straightforward way to inject domain knowledge but often degrades the model's generality. In contrast, on-policy reinforcement learning (RL) preserves generality but fails to effectively assimilate hard samples that exceed the model's current reasoning level. Recent off-policy RL attempts improve hard sample utilization, yet they suffer from severe training instability due to the forced distribution shift toward off-policy knowledge. To reconcile effective off-policy knowledge absorption with the stability of on-policy RL, we propose Rephrasing Policy Optimization (RePO). In RePO, the policy model is prompted to first comprehend off-policy knowledge and then rephrase it into trajectories that conform to its own stylistic and parametric distribution. RePO dynamically replaces low-reward rollouts with these rephrased, high-quality trajectories. This strategy guides the model toward correct reasoning paths while strictly preserving on-policy training dynamics. Experiments on several benchmarks demonstrate that RePO improves hard-sample utilization and outperforms existing baselines, achieving state-of-the-art performance.

Large language models split into two families: reasoning-centric LLMs, which strengthen internal chain-of-thought reasoning but cannot invoke external tools, and agentic LLMs, which learn to interact with environments and leverage tools but often lag in deep reasoning. This divide arises from fundamentally different training objectives, leading to mismatched strengths and inefficiency on simple queries, where both families tend to overthink or over-call tools. In this work, we present Adaptive Agent Foundation Model (A^2FM), a unified framework that follows a route-then-align principle: the model first learns task-aware routing and then aligns mode-specific trajectories under a shared backbone. To address the inefficiency gap, we introduce a third mode-instant-that handles simple queries directly, preventing unnecessary reasoning or tool calls while complementing the agentic and reasoning modes. To jointly enhance accuracy and efficiency, we propose Adaptive Policy Optimization (APO), which enforces adaptive sampling across modes and applies a cost-regularized reward. On the 32B scale, A^2FM achieves 13.4% on BrowseComp, 70.4% on AIME25, and 16.7% on HLE, setting new SOTA among comparable models and performing competitively with frontier LLMs across agentic, reasoning, and general benchmarks. Notably, the adaptive execution achieves a cost of pass of only $0.00487 per correct answer-cutting cost by 45.2% relative to reasoning and 33.5% relative to agentic, thus delivering substantially higher cost efficiency while maintaining comparable accuracy.

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.

Reinforcement Learning with Verifiable Rewards has recently advanced the capabilities of Large Language Models in complex reasoning tasks by providing explicit rule-based supervision. Among RLVR methods, GRPO and its variants have achieved strong empirical performance. Despite their success, we identify that they suffer from Gradient Misassignment in Positives and Gradient Domination in Negatives, which lead to inefficient and suboptimal policy updates. To address these issues, we propose Rewards as Labels (REAL), a novel framework that revisits verifiable rewards as categorical labels rather than scalar weights, thereby reformulating policy optimization as a classification problem. Building on this, we further introduce anchor logits to enhance policy learning. Our analysis reveals that REAL induces a monotonic and bounded gradient weighting, enabling balanced gradient allocation across rollouts and effectively mitigating the identified mismatches. Extensive experiments on mathematical reasoning benchmarks show that REAL improves training stability and consistently outperforms GRPO and strong variants such as DAPO. On the 1.5B model, REAL improves average Pass@1 over DAPO by 6.7%. These gains further scale to 7B model, REAL continues to outperform DAPO and GSPO by 6.2% and 1.7%, respectively. Notably, even with a vanilla binary cross-entropy, REAL remains stable and exceeds DAPO by 4.5% on average.

While scaling the length of responses at test-time has been shown to markedly improve the reasoning abilities and performance of large language models (LLMs), it often results in verbose outputs and increases inference cost. Prior approaches for efficient test-time scaling, typically using universal budget constraints or query-level length optimization, do not leverage historical information from previous encounters with the same problem during training. We hypothesize that this limits their ability to progressively make solutions more concise over time. To address this, we present History-Aware Policy Optimization (HAPO), which keeps track of a history state (e.g., the minimum length over previously generated correct responses) for each problem. HAPO employs a novel length reward function based on this history state to incentivize the discovery of correct solutions that are more concise than those previously found. Crucially, this reward structure avoids overly penalizing shorter incorrect responses with the goal of facilitating exploration towards more efficient solutions. By combining this length reward with a correctness reward, HAPO jointly optimizes for correctness and efficiency. We use HAPO to train DeepSeek-R1-Distill-Qwen-1.5B, DeepScaleR-1.5B-Preview, and Qwen-2.5-1.5B-Instruct, and evaluate HAPO on several math benchmarks that span various difficulty levels. Experiment results demonstrate that HAPO effectively induces LLMs' concise reasoning abilities, producing length reductions of 33-59% with accuracy drops of only 2-5%.

While large language models (LLMs) have demonstrated strong performance on factoid question answering, they are still prone to hallucination and untruthful responses, particularly when tasks demand information outside their parametric knowledge. Indeed, truthfulness requires more than accuracy -- models must also recognize uncertainty and abstain when unsure to avoid hallucinations. This presents a fundamental challenge for existing methods: approaches that optimize for accuracy often amplify hallucinations, while those that encourage abstention can become overly conservative, sacrificing correct answers. Both extremes ultimately compromise truthfulness. In this work, we present TruthRL, a general reinforcement learning (RL) framework that directly optimizes the truthfulness of LLMs. Specifically, we implement TruthRL using GRPO with a simple yet effective ternary reward that distinguishes correct answers, hallucinations, and abstentions. It incentivizes models to reduce hallucinations not only by providing correct responses, but also by enabling abstention when uncertain, thereby improving truthfulness. Extensive experiments across four knowledge-intensive benchmarks show that, compared to vanilla RL, TruthRL significantly reduces hallucinations by 28.9% and improves truthfulness by 21.1%, with consistent gains across various backbone models (e.g., Qwen, Llama) under both retrieval and non-retrieval setups. In-depth ablation study demonstrates that vanilla accuracy-driven methods, such as supervised fine-tuning or RL with a binary reward, struggle to balance factual correctness and uncertainty. In contrast, our proposed truthfulness-driven TruthRL achieves strong performance in both accuracy and truthfulness, underscoring the importance of learning objective design for developing truthful LLMs.

In real-world applications of reinforcement learning, it is often challenging to obtain a state representation that is parsimonious and satisfies the Markov property without prior knowledge. Consequently, it is common practice to construct a state larger than necessary, e.g., by concatenating measurements over contiguous time points. However, needlessly increasing the dimension of the state may slow learning and obfuscate the learned policy. We introduce the notion of a minimal sufficient state in a Markov decision process (MDP) as the subvector of the original state under which the process remains an MDP and shares the same reward function as the original process. We propose a novel SEquEntial Knockoffs (SEEK) algorithm that estimates the minimal sufficient state in a system with high-dimensional complex nonlinear dynamics. In large samples, the proposed method achieves selection consistency. As the method is agnostic to the reinforcement learning algorithm being applied, it benefits downstream tasks such as policy learning. Empirical experiments verify theoretical results and show the proposed approach outperforms several competing methods regarding variable selection accuracy and regret.

While Reinforcement Learning for Verifiable Rewards (RLVR) is powerful for training large reasoning models, its training dynamics harbor a critical challenge: RL overfitting, where models gain training rewards but lose generalization. Our analysis reveals this is driven by policy over-specialization and catastrophic forgetting of diverse solutions generated during training. Standard optimization discards this valuable inter-step policy diversity. To address this, we introduce RLoop, a self-improving framework built on iterative policy initialization. RLoop transforms the standard training process into a virtuous cycle: it first uses RL to explore the solution space from a given policy, then filters the successful trajectories to create an expert dataset. This dataset is used via Rejection-sampling Fine-Tuning (RFT) to refine the initial policy, creating a superior starting point for the next iteration. This loop of exploration and exploitation via iterative re-initialization effectively converts transient policy variations into robust performance gains. Our experiments show RLoop mitigates forgetting and substantially improves generalization, boosting average accuracy by 9% and pass@32 by over 15% compared to vanilla RL.

In long-horizon tasks, recent agents based on Large Language Models (LLMs) face a significant challenge that sparse, outcome-based rewards make it difficult to assign credit to intermediate steps. Previous methods mainly focus on creating dense reward signals to guide learning, either through traditional reinforcement learning techniques like inverse reinforcement learning or by using Process Reward Models for step-by-step feedback. In this paper, we identify a fundamental problem in the learning dynamics of LLMs: the magnitude of policy gradients is inherently coupled with the entropy, which leads to inefficient small updates for confident correct actions and potentially destabilizes large updates for uncertain ones. To resolve this, we propose Entropy-Modulated Policy Gradients (EMPG), a framework that re-calibrates the learning signal based on step-wise uncertainty and the final task outcome. EMPG amplifies updates for confident correct actions, penalizes confident errors, and attenuates updates from uncertain steps to stabilize exploration. We further introduce a bonus term for future clarity that encourages agents to find more predictable solution paths. Through comprehensive experiments on three challenging agent tasks, WebShop, ALFWorld, and Deep Search, we demonstrate that EMPG achieves substantial performance gains and significantly outperforms strong policy gradient baselines. Project page is at https://empgseed-seed.github.io/

Reinforcement learning has significantly enhanced the reasoning capabilities of Large Language Models (LLMs) in complex problem-solving tasks. Recently, the introduction of DeepSeek R1 has inspired a surge of interest in leveraging rule-based rewards as a low-cost alternative for computing advantage functions and guiding policy optimization. However, a common challenge observed across many replication and extension efforts is that when multiple sampled responses under a single prompt converge to identical outcomes, whether correct or incorrect, the group-based advantage degenerates to zero. This leads to vanishing gradients and renders the corresponding samples ineffective for learning, ultimately limiting training efficiency and downstream performance. To address this issue, we propose a consistency-aware policy optimization framework that introduces a structured global reward based on outcome consistency, the global loss based on it ensures that, even when model outputs show high intra-group consistency, the training process still receives meaningful learning signals, which encourages the generation of correct and self-consistent reasoning paths from a global perspective. Furthermore, we incorporate an entropy-based soft blending mechanism that adaptively balances local advantage estimation with global optimization, enabling dynamic transitions between exploration and convergence throughout training. Our method introduces several key innovations in both reward design and optimization strategy. We validate its effectiveness through substantial performance gains on multiple mathematical reasoning benchmarks, highlighting the proposed framework's robustness and general applicability. Code of this work has been released at https://github.com/hijih/copo-code.git.

As Reinforcement Learning (RL) agents are increasingly employed in diverse decision-making problems using reward preferences, it becomes important to ensure that policies learned by these frameworks in mapping observations to a probability distribution of the possible actions are explainable. However, there is little to no work in the systematic understanding of these complex policies in a contrastive manner, i.e., what minimal changes to the policy would improve/worsen its performance to a desired level. In this work, we present COUNTERPOL, the first framework to analyze RL policies using counterfactual explanations in the form of minimal changes to the policy that lead to the desired outcome. We do so by incorporating counterfactuals in supervised learning in RL with the target outcome regulated using desired return. We establish a theoretical connection between Counterpol and widely used trust region-based policy optimization methods in RL. Extensive empirical analysis shows the efficacy of COUNTERPOL in generating explanations for (un)learning skills while keeping close to the original policy. Our results on five different RL environments with diverse state and action spaces demonstrate the utility of counterfactual explanations, paving the way for new frontiers in designing and developing counterfactual policies.

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.

While reinforcement learning (RL) shows promise in training tool-use large language models (LLMs) using verifiable outcome rewards, existing methods largely overlook the potential of explicit reasoning rewards to bolster reasoning and tool utilization. Furthermore, natively combining reasoning and outcome rewards may yield suboptimal performance or conflict with the primary optimization objective. To address this, we propose advantage-weighted policy optimization (AWPO) -- a principled RL framework that effectively integrates explicit reasoning rewards to enhance tool-use capability. AWPO incorporates variance-aware gating and difficulty-aware weighting to adaptively modulate advantages from reasoning signals based on group-relative statistics, alongside a tailored clipping mechanism for stable optimization. Extensive experiments demonstrate that AWPO achieves state-of-the-art performance across standard tool-use benchmarks, significantly outperforming strong baselines and leading closed-source models in challenging multi-turn scenarios. Notably, with exceptional parameter efficiency, our 4B model surpasses Grok-4 by 16.0 percent in multi-turn accuracy while preserving generalization capability on the out-of-distribution MMLU-Pro benchmark.

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.

Proximal Policy Optimization (PPO) has become the predominant algorithm for on-policy reinforcement learning due to its scalability and empirical robustness across domains. However, there is a significant disconnect between the underlying foundations of trust region methods and the heuristic clipped objective used in PPO. In this paper, we bridge this gap by introducing the Bounded Ratio Reinforcement Learning (BRRL) framework. We formulate a novel regularized and constrained policy optimization problem and derive its analytical optimal solution. We prove that this solution ensures monotonic performance improvement. To handle parameterized policy classes, we develop a policy optimization algorithm called Bounded Policy Optimization (BPO) that minimizes an advantage-weighted divergence between the policy and the analytic optimal solution from BRRL. We further establish a lower bound on the expected performance of the resulting policy in terms of the BPO loss function. Notably, our framework also provides a new theoretical lens to interpret the success of the PPO loss, and connects trust region policy optimization and the Cross-Entropy Method (CEM). We additionally extend BPO to Group-relative BPO (GBPO) for LLM fine-tuning. Empirical evaluations of BPO across MuJoCo, Atari, and complex IsaacLab environments (e.g., Humanoid locomotion), and of GBPO for LLM fine-tuning tasks, demonstrate that BPO and GBPO generally match or outperform PPO and GRPO in stability and final performance.

Large language models (LLMs) struggle with complex, long-horizon reasoning due to instability caused by their frozen policy assumption. Current test-time scaling methods treat execution feedback merely as an external signal for filtering or rewriting trajectories, without internalizing it to improve the underlying reasoning strategy. Inspired by Popper's epistemology of "conjectures and refutations," we argue that intelligence requires real-time evolution of the model's policy through learning from failed attempts. We introduce Policy of Thoughts (PoT), a framework that recasts reasoning as a within-instance online optimization process. PoT first generates diverse candidate solutions via an efficient exploration mechanism, then uses Group Relative Policy Optimization (GRPO) to update a transient LoRA adapter based on execution feedback. This closed-loop design enables dynamic, instance-specific refinement of the model's reasoning priors. Experiments show that PoT dramatically boosts performance: a 4B model achieves 49.71% accuracy on LiveCodeBench, outperforming GPT-4o and DeepSeek-V3 despite being over 50 smaller.

Reinforcement learning fine-tuning (RLFT) is a dominant paradigm for improving pretrained policies for downstream tasks. These pretrained policies, trained on large datasets, produce generations with a broad range of promising but unrefined behaviors. Often, a critical failure mode of RLFT arises when policies lose this diversity and collapse into a handful of easily exploitable outputs. This convergence hinders exploration, which is essential for expanding the capabilities of the pretrained policy and for amplifying the benefits of test-time compute scaling. To address this, we introduce an objective for policy gradient methods that explicitly enforces the exploration and refinement of diverse generations, which we call a polychromic objective. We then show how proximal policy optimization (PPO) can be adapted to optimize this objective. Our method (1) employs vine sampling to collect on-policy rollouts and (2) modifies the advantage function to reflect the advantage under our new objective. Experiments on BabyAI, Minigrid, and Algorithmic Creativity show that our method improves success rates by reliably solving a larger set of environment configurations and generalizes better under large perturbations. Moreover, when given multiple attempts in pass@k experiments, the policy achieves substantially higher coverage, demonstrating its ability to maintain and exploit a diverse repertoire of strategies.

Training stability remains a central challenge in reinforcement learning (RL) for large language models (LLMs). Policy staleness, asynchronous training, and mismatches between training and inference engines all cause the behavior policy to diverge from the current policy, risking training collapse. Importance sampling provides a principled correction for this distribution shift but suffers from high variance; existing remedies such as token-level clipping and sequence-level normalization lack a unified theoretical foundation. We propose Variational sEquence-level Soft Policy Optimization (VESPO). By incorporating variance reduction into a variational formulation over proposal distributions, VESPO derives a closed-form reshaping kernel that operates directly on sequence-level importance weights without length normalization. Experiments on mathematical reasoning benchmarks show that VESPO maintains stable training under staleness ratios up to 64x and fully asynchronous execution, and delivers consistent gains across both dense and Mixture-of-Experts models. Code is available at https://github.com/FloyedShen/VESPO

Policy constraint methods to offline reinforcement learning (RL) typically utilize parameterization or regularization that constrains the policy to perform actions within the support set of the behavior policy. The elaborative designs of parameterization methods usually intrude into the policy networks, which may bring extra inference cost and cannot take full advantage of well-established online methods. Regularization methods reduce the divergence between the learned policy and the behavior policy, which may mismatch the inherent density-based definition of support set thereby failing to avoid the out-of-distribution actions effectively. This paper presents Supported Policy OpTimization (SPOT), which is directly derived from the theoretical formalization of the density-based support constraint. SPOT adopts a VAE-based density estimator to explicitly model the support set of behavior policy and presents a simple but effective density-based regularization term, which can be plugged non-intrusively into off-the-shelf off-policy RL algorithms. SPOT achieves the state-of-the-art performance on standard benchmarks for offline RL. Benefiting from the pluggable design, offline pretrained models from SPOT can also be applied to perform online fine-tuning seamlessly.

Causal autoregressive video diffusion models support real-time streaming generation by extrapolating future chunks from previously generated content. Distilling such generators from high-fidelity bidirectional teachers yields competitive few-step models, yet a persistent gap between the history distributions encountered during training and those arising at inference constrains generation quality over long horizons. We introduce the Real-time Autoregressive Video Extrapolation Network (RAVEN), a training-time test framework that repacks each self rollout into an interleaved sequence of clean historical endpoints and noisy denoising states. This formulation aligns training attention with inference-time extrapolation and allows downstream chunk losses to supervise the history representations on which future predictions depend. We further propose Consistency-model Group Relative Policy Optimization (CM-GRPO), which reformulates a consistency sampling step as a conditional Gaussian transition and applies online Reinforcement Learning (RL) directly to this kernel, avoiding the Euler-Maruyama auxiliary process adopted in prior flow-model RL formulations. Experiments demonstrate that RAVEN surpasses recent causal video distillation baselines across quality, semantic, and dynamic degree evaluations, and that CM-GRPO provides further gains when combined with RAVEN.

Real-world user requests to LLM agents are often underspecified. Agents must interact to acquire missing information and make correct downstream decisions. However, current multi-turn GRPO-based methods often rely on trajectory-level reward computation, which leads to credit assignment problems and insufficient advantage signals within rollout groups. A feasible approach is to identify valuable interaction turns at a fine granularity to drive more targeted learning. To address this, we introduce InfoPO (Information-Driven Policy Optimization), which frames multi-turn interaction as a process of active uncertainty reduction and computes an information-gain reward that credits turns whose feedback measurably changes the agent's subsequent action distribution compared to a masked-feedback counterfactual. It then combines this signal with task outcomes via an adaptive variance-gated fusion to identify information importance while maintaining task-oriented goal direction. Across diverse tasks, including intent clarification, collaborative coding, and tool-augmented decision making, InfoPO consistently outperforms prompting and multi-turn RL baselines. It also demonstrates robustness under user simulator shifts and generalizes effectively to environment-interactive tasks. Overall, InfoPO provides a principled and scalable mechanism for optimizing complex agent-user collaboration. Code is available at https://github.com/kfq20/InfoPO.

Reinforcement learning has become a cornerstone technique for developing reasoning models in complex tasks, ranging from mathematical problem-solving to imaginary reasoning. The optimization of these models typically relies on policy gradient methods, whose efficacy hinges on the accurate estimation of an advantage function. However, prevailing methods typically employ static advantage estimation, a practice that leads to inefficient credit assignment by neglecting the dynamic utility of training samples over time. This limitation results in suboptimal policy updates, which in turn manifest as slower convergence rates and increased learning instability, as models fail to adapt to evolving sample utilities effectively. To address this problem, we introduce ADORA (Advantage Dynamics via Online Rollout Adaptation), a novel framework for policy optimization. ADORA dynamically adjusts the advantage function's weighting by adaptively categorizing training data into temporarily advantageous and disadvantageous samples, based on their evolving utility during online model rollouts. This tailored data differentiation strategy allows ADORA to be seamlessly integrated into existing policy optimization algorithms without significant architectural modifications, enabling the policy to prioritize learning from more informative experiences and thereby achieve more efficient policy updates. Extensive evaluations across diverse model families and varying data scales demonstrate that ADORA is a robust and efficient framework. It significantly enhances long reasoning in both geometric and mathematical tasks, consistently achieving notable performance gains without requiring sensitive hyperparameter tuning.

This paper introduces Completion Pruning Policy Optimization (CPPO) to accelerate the training of reasoning models based on Group Relative Policy Optimization (GRPO). GRPO, while effective, incurs high training costs due to the need for sampling multiple completions for each question. Our experiment and theoretical analysis reveals that the number of completions impacts model accuracy yet increases training time multiplicatively, and not all completions contribute equally to policy training -- their contribution depends on their relative advantage. To address these issues, we propose CPPO, which prunes completions with low absolute advantages, significantly reducing the number needed for gradient calculation and updates. Additionally, we introduce a dynamic completion allocation strategy to maximize GPU utilization by incorporating additional questions, further enhancing training efficiency. Experimental results demonstrate that CPPO achieves up to 8.32times speedup on GSM8K and 3.51times on Math while preserving or even enhancing the accuracy compared to the original GRPO. We release our code at https://github.com/lzhxmu/CPPO.

Real-time robotic control demands fast action generation. However, existing generative policies based on diffusion and flow matching require multi-step sampling, fundamentally limiting deployment in time-critical scenarios. We propose Dispersive MeanFlow Policy Optimization (DMPO), a unified framework that enables true one-step generation through three key components: MeanFlow for mathematically-derived single-step inference without knowledge distillation, dispersive regularization to prevent representation collapse, and reinforcement learning (RL) fine-tuning to surpass expert demonstrations. Experiments across RoboMimic manipulation and OpenAI Gym locomotion benchmarks demonstrate competitive or superior performance compared to multi-step baselines. With our lightweight model architecture and the three key algorithmic components working in synergy, DMPO exceeds real-time control requirements (>120Hz) with 5-20x inference speedup, reaching hundreds of Hertz on high-performance GPUs. Physical deployment on a Franka-Emika-Panda robot validates real-world applicability.

Asynchronous reinforcement learning improves rollout throughput for large language model agents by decoupling sample generation from policy optimization, but it also introduces a critical failure mode for PPO-style off-policy correction. In heterogeneous training systems, the total importance ratio should ideally be decomposed into two semantically distinct factors: a training--inference discrepancy term that aligns inference-side and training-side distributions at the same behavior-policy version, and a policy-staleness term that constrains the update from the historical policy to the current policy. We show that practical asynchronous pipelines with delayed updates and partial rollouts often lose the required historical training-side logits, or old logits. This missing-old-logit problem entangles discrepancy repair with staleness correction, breaks the intended semantics of decoupled correction, and makes clipping and masking thresholds interact undesirably. To address this issue, we study both exact and approximate correction routes. We propose three exact old-logit acquisition strategies: snapshot-based version tracking, a dedicated old-logit model, and synchronization via partial rollout interruption, and compare their system trade-offs. From the perspective of approximate correction, we focus on preserving the benefits of decoupled correction through a more appropriate approximate policy when exact old logits cannot be recovered at low cost, without incurring extra system overhead. Following this analysis, we adopt a revised PPO-EWMA method, which achieves significant gains in both training speed and optimization performance. Code at https://github.com/millioniron/ROLL.

The alignment of language models with human preferences is vital for their application in real-world tasks. The problem is formulated as optimizing the model's policy to maximize the expected reward that reflects human preferences with minimal deviation from the initial policy. While considered as a straightforward solution, reinforcement learning (RL) suffers from high variance in policy updates, which impedes efficient policy improvement. Recently, direct preference optimization (DPO) was proposed to directly optimize the policy from preference data. Though simple to implement, DPO is derived based on the optimal policy that is not assured to be achieved in practice, which undermines its convergence to the intended solution. In this paper, we propose efficient exact optimization (EXO) of the alignment objective. We prove that EXO is guaranteed to optimize in the same direction as the RL algorithms asymptotically for arbitary parametrization of the policy, while enables efficient optimization by circumventing the complexities associated with RL algorithms. We compare our method to DPO with both theoretical and empirical analyses, and further demonstrate the advantages of our method over existing approaches on realistic human preference data.

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.

We present Future-KL Influenced Policy Optimization (FIPO), a reinforcement learning algorithm designed to overcome reasoning bottlenecks in large language models. While GRPO style training scales effectively, it typically relies on outcome-based rewards (ORM) that distribute a global advantage uniformly across every token in a trajectory. We argue that this coarse-grained credit assignment imposes a performance ceiling by failing to distinguish critical logical pivots from trivial tokens. FIPO addresses this by incorporating discounted future-KL divergence into the policy update, creating a dense advantage formulation that re-weights tokens based on their influence on subsequent trajectory behavior. Empirically, FIPO enables models to break through the length stagnation seen in standard baselines. Evaluated on Qwen2.5-32B, FIPO extends the average chain-of-thought length from roughly 4,000 to over 10,000 tokens and increases AIME 2024 Pass@1 accuracy from 50.0% to a peak of 58.0% (converging at approximately 56.0\%). This outperforms both DeepSeek-R1-Zero-Math-32B (around 47.0%) and o1-mini (approximately 56.0%). Our results suggest that establishing dense advantage formulations is a vital path for evolving ORM-based algorithms to unlock the full reasoning potential of base models. We open-source our training system, built on the verl framework.

Proximal constraints are fundamental to the stability of the Large Language Model reinforcement learning. While the canonical clipping mechanism in PPO serves as an efficient surrogate for trust regions, we identify a critical bottleneck: fixed bounds strictly constrain the upward update margin of low-probability actions, disproportionately suppressing high-advantage tail strategies and inducing rapid entropy collapse. To address this, we introduce Band-constrained Policy Optimization (BandPO). BandPO replaces canonical clipping with Band, a unified theoretical operator that projects trust regions defined by f-divergences into dynamic, probability-aware clipping intervals. Theoretical analysis confirms that Band effectively resolves this exploration bottleneck. We formulate this mapping as a convex optimization problem, guaranteeing a globally optimal numerical solution while deriving closed-form solutions for specific divergences. Extensive experiments across diverse models and datasets demonstrate that BandPO consistently outperforms canonical clipping and Clip-Higher, while robustly mitigating entropy collapse.

Interactive digital agents (IDAs) leverage APIs of stateful digital environments to perform tasks in response to user requests. While IDAs powered by instruction-tuned large language models (LLMs) can react to feedback from interface invocations in multi-step exchanges, they have not been trained in their respective digital environments. Prior methods accomplish less than half of tasks in sophisticated benchmarks such as AppWorld. We present a reinforcement learning (RL) approach that trains IDAs directly in their target environments. We formalize this training as a partially observable Markov decision process and derive LOOP, a data- and memory-efficient variant of proximal policy optimization. LOOP uses no value network and maintains exactly one copy of the underlying LLM in memory, making its implementation straightforward and as memory-efficient as fine-tuning a single LLM. A 32-billion-parameter agent trained with LOOP in the AppWorld environment outperforms the much larger OpenAI o1 agent by 9 percentage points (15% relative). To our knowledge, this is the first reported application of RL to IDAs that interact with a stateful, multi-domain, multi-app environment via direct API calls. Our analysis sheds light on the effectiveness of RL in this area, showing that the agent learns to consult the API documentation, avoid unwarranted assumptions, minimize confabulation, and recover from setbacks.

The application of Reinforcement Learning with Verifiable Rewards (RLVR) to mathematical and coding domains has demonstrated significant improvements in the reasoning and problem-solving abilities of Large Language Models. Despite its success in single generation problem solving, the reinforcement learning fine-tuning process may harm the model's exploration ability, as reflected in decreased diversity of generations and a resulting degradation of performance during Best-of-N sampling for large N values. In this work, we focus on optimizing the max@k metric, a continuous generalization of pass@k. We derive an unbiased on-policy gradient estimate for direct optimization of this metric. Furthermore, we extend our derivations to the off-policy updates, a common element in modern RLVR algorithms, that allows better sample efficiency. Empirically, we show that our objective effectively optimizes max@k metric in off-policy scenarios, aligning the model with the Best-of-N inference strategy.

Reinforcement Learning has emerged as a post-training approach to elicit agentic RAG behaviors such as search and planning from language models. However, compact language models (e.g., 0.5B parameters) struggle due to poor reasoning ability, resulting in sparse rewards and unstable training. To overcome these difficulties, we propose Distillation-Guided Policy Optimization (DGPO), which addresses the challenges through cold-start initialization from teacher demonstrations and continuous teacher guidance during policy optimization. To systematically evaluate our approach, we introduce Agentic RAG Capabilities (ARC), a fine-grained metric analyzing reasoning, search coordination, and response synthesis. Comprehensive experiments demonstrate that DGPO enables compact models to achieve sophisticated agentic search behaviors, even outperforming the larger teacher model in some cases. DGPO makes agentic RAG feasible in computing resource-constrained environments.

Multi-Objective Reinforcement Learning (MORL) is a generalization of traditional Reinforcement Learning (RL) that aims to optimize multiple, often conflicting objectives simultaneously rather than focusing on a single reward. This approach is crucial in complex decision-making scenarios where agents must balance trade-offs between various goals, such as maximizing performance while minimizing costs. We consider the problem of MORL where the objectives are combined using a non-linear scalarization function. Just like in standard RL, policy gradient methods (PGMs) are amongst the most effective for handling large and continuous state-action spaces in MORL. However, existing PGMs for MORL suffer from high sample inefficiency, requiring large amounts of data to be effective. Previous attempts to solve this problem rely on overly strict assumptions, losing PGMs' benefits in scalability to large state-action spaces. In this work, we address the issue of sample efficiency by implementing variance-reduction techniques to reduce the sample complexity of policy gradients while maintaining general assumptions.

Large language models (LLMs) often hallucinate, yet most existing fact-checking methods treat factuality evaluation as a binary classification problem, offering limited interpretability and failing to capture fine-grained error types. In this paper, we introduce InFi-Check, a framework for interpretable and fine-grained fact-checking of LLM outputs. Specifically, we first propose a controlled data synthesis pipeline that generates high-quality data featuring explicit evidence, fine-grained error type labels, justifications, and corrections. Based on this, we further construct large-scale training data and a manually verified benchmark InFi-Check-FG for fine-grained fact-checking of LLM outputs. Building on these high-quality training data, we further propose InFi-Checker, which can jointly provide supporting evidence, classify fine-grained error types, and produce justifications along with corrections. Experiments show that InFi-Checker achieves state-of-the-art performance on InFi-Check-FG and strong generalization across various downstream tasks, significantly improving the utility and trustworthiness of factuality evaluation.

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.

Recent advances in large language models (LLMs) have greatly improved their reasoning and decision-making abilities when deployed as agents. Richer reasoning, however, often comes at the cost of longer chain of thought (CoT), hampering interaction efficiency in real-world scenarios. Nevertheless, there still lacks systematic definition of LLM agent efficiency, hindering targeted improvements. To this end, we introduce dual-efficiency, comprising (i) step-level efficiency, which minimizes tokens per step, and (ii) trajectory-level efficiency, which minimizes the number of steps to complete a task. Building on this definition, we propose DEPO, a dual-efficiency preference optimization method that jointly rewards succinct responses and fewer action steps. Experiments on WebShop and BabyAI show that DEPO cuts token usage by up to 60.9% and steps by up to 26.9%, while achieving up to a 29.3% improvement in performance. DEPO also generalizes to three out-of-domain math benchmarks and retains its efficiency gains when trained on only 25% of the data. Our project page is at https://opencausalab.github.io/DEPO.

Policy gradient methods hold great potential for solving complex continuous control tasks. Still, their training efficiency can be improved by exploiting structure within the optimization problem. Recent work indicates that supervised learning can be accelerated by leveraging the fact that gradients lie in a low-dimensional and slowly-changing subspace. In this paper, we conduct a thorough evaluation of this phenomenon for two popular deep policy gradient methods on various simulated benchmark tasks. Our results demonstrate the existence of such gradient subspaces despite the continuously changing data distribution inherent to reinforcement learning. These findings reveal promising directions for future work on more efficient reinforcement learning, e.g., through improving parameter-space exploration or enabling second-order optimization.

Reinforcement Learning with Verifiable Rewards (RLVR) has proven effective for enhancing the reasoning capabilities of Large Language Models (LLMs). However, dominant approaches like Group Relative Policy Optimization (GRPO) face critical stability challenges: they suffer from high estimator variance under computational constraints (small group sizes) and vanishing gradient signals in saturated failure regimes where all responses yield identical zero rewards. To address this, we propose Empirical Bayes Policy Optimization (EBPO), a novel framework that regularizes local group-based baselines by borrowing strength from the policy's accumulated global statistics. Instead of estimating baselines in isolation, EBPO employs a shrinkage estimator that dynamically balances local group statistics with a global prior updated via Welford's online algorithm. Theoretically, we demonstrate that EBPO guarantees strictly lower Mean Squared Error (MSE), bounded entropy decay, and non-vanishing penalty signals in failure scenarios compared to GRPO. Empirically, EBPO consistently outperforms GRPO and other established baselines across diverse benchmarks, including AIME and OlympiadBench. Notably, EBPO exhibits superior training stability, achieving high-performance gains even with small group sizes, and benefits significantly from difficulty-stratified curriculum learning.

Hybrid RL is the setting where an RL agent has access to both offline data and online data by interacting with the real-world environment. In this work, we propose a new hybrid RL algorithm that combines an on-policy actor-critic method with offline data. On-policy methods such as policy gradient and natural policy gradient (NPG) have shown to be more robust to model misspecification, though sometimes it may not be as sample efficient as methods that rely on off-policy learning. On the other hand, offline methods that depend on off-policy training often require strong assumptions in theory and are less stable to train in practice. Our new approach integrates a procedure of off-policy training on the offline data into an on-policy NPG framework. We show that our approach, in theory, can obtain a best-of-both-worlds type of result -- it achieves the state-of-art theoretical guarantees of offline RL when offline RL-specific assumptions hold, while at the same time maintaining the theoretical guarantees of on-policy NPG regardless of the offline RL assumptions' validity. Experimentally, in challenging rich-observation environments, we show that our approach outperforms a state-of-the-art hybrid RL baseline which only relies on off-policy policy optimization, demonstrating the empirical benefit of combining on-policy and off-policy learning. Our code is publicly available at https://github.com/YifeiZhou02/HNPG.

Reinforcement learning (RL) approaches for Large Language Models (LLMs) frequently use on-policy algorithms, such as PPO or GRPO. However, policy lag from distributed training architectures and differences between the training and inference policies break this assumption, making the data off-policy by design. To rectify this, prior work has focused on making this off-policy data appear more on-policy, either via importance sampling (IS), or by more closely aligning the training and inference policies by explicitly modifying the inference engine. In this work, we embrace off-policyness and propose a novel off-policy RL algorithm that does not require these modifications: Optimal Advantage-based Policy Optimization with Lagged Inference policy (OAPL). We show that OAPL outperforms GRPO with importance sampling on competition math benchmarks, and can match the performance of a publicly available coding model, DeepCoder, on LiveCodeBench, while using 3x fewer generations during training. We further empirically demonstrate that models trained via OAPL have improved test time scaling under the Pass@k metric. OAPL allows for efficient, effective post-training even with lags of more than 400 gradient steps between the training and inference policies, 100x more off-policy than prior approaches.

In real-world scenarios, the application of reinforcement learning is significantly challenged by complex non-stationarity. Most existing methods attempt to model changes in the environment explicitly, often requiring impractical prior knowledge of environments. In this paper, we propose a new perspective, positing that non-stationarity can propagate and accumulate through complex causal relationships during state transitions, thereby compounding its sophistication and affecting policy learning. We believe that this challenge can be more effectively addressed by implicitly tracing the causal origin of non-stationarity. To this end, we introduce the Causal-Origin REPresentation (COREP) algorithm. COREP primarily employs a guided updating mechanism to learn a stable graph representation for the state, termed as causal-origin representation. By leveraging this representation, the learned policy exhibits impressive resilience to non-stationarity. We supplement our approach with a theoretical analysis grounded in the causal interpretation for non-stationary reinforcement learning, advocating for the validity of the causal-origin representation. Experimental results further demonstrate the superior performance of COREP over existing methods in tackling non-stationarity problems.

Proximal Policy Optimization (PPO) is central to aligning Large Language Models (LLMs) in reasoning tasks with verifiable rewards. However, standard token-level PPO struggles in this setting due to the instability of temporal credit assignment over long Chain-of-Thought (CoT) horizons and the prohibitive memory cost of the value model. While critic-free alternatives like GRPO mitigate these issues, they incur significant computational overhead by requiring multiple samples for baseline estimation, severely limiting training throughput. In this paper, we introduce Sequence-Level PPO (SPPO), a scalable algorithm that harmonizes the sample efficiency of PPO with the stability of outcome-based updates. SPPO reformulates the reasoning process as a Sequence-Level Contextual Bandit problem, employing a decoupled scalar value function to derive low-variance advantage signals without multi-sampling. Extensive experiments on mathematical benchmarks demonstrate that SPPO significantly surpasses standard PPO and matches the performance of computation-heavy group-based methods, offering a resource-efficient framework for aligning reasoning LLMs.