Daily Papers

Existing Multimodal Large Language Models (MLLMs) suffer from significant performance degradation on the long document understanding task as document length increases. This stems from two fundamental challenges: 1) a low Signal-to-Noise Ratio (SNR), with crucial evidence buried in irrelevant pages; and 2) supervision scarcity, as datasets offering only final short answers provide a weak learning signal. In this paper, we address these challenges by proposing a paradigm that requires the model to execute a structured Analysis, Localization and Reasoning workflow. To instill this capability, we design a two-stage training framework: we first perform Supervised Fine-Tuning on high-quality data generated via an efficient knowledge distillation strategy. Subsequently, we employ an Evidence-aware Group Relative Policy Optimization which jointly optimizes for both evidence localization and answer accuracy. Additionally, we introduce a Evidence-Guided Resolution Allocation strategy to mitigate memory constraints of training on multi-pages documents. Extensive experiments demonstrate that DocSeeker achieves superior performance on both in-domain and out-of-domain tasks. We show it robustly generalizes from short-page training to ultra-long documents and is naturally synergistic with visual Retrieval-Augmented Generation systems, serving as a solid foundation for their implementation.

Reinforcement learning (RL) has emerged as a critical technique for enhancing LLM-based deep search agents. However, existing approaches primarily rely on binary outcome rewards, which fail to capture the comprehensiveness and factuality of agents' reasoning process, and often lead to undesirable behaviors such as shortcut exploitation and hallucinations. To address these limitations, we propose Citation-aware Rubric Rewards (CaRR), a fine-grained reward framework for deep search agents that emphasizes reasoning comprehensiveness, factual grounding, and evidence connectivity. CaRR decomposes complex questions into verifiable single-hop rubrics and requires agents to satisfy these rubrics by explicitly identifying hidden entities, supporting them with correct citations, and constructing complete evidence chains that link to the predicted answer. We further introduce Citation-aware Group Relative Policy Optimization (C-GRPO), which combines CaRR and outcome rewards for training robust deep search agents. Experiments show that C-GRPO consistently outperforms standard outcome-based RL baselines across multiple deep search benchmarks. Our analysis also validates that C-GRPO effectively discourages shortcut exploitation, promotes comprehensive, evidence-grounded reasoning, and exhibits strong generalization to open-ended deep research tasks. Our code and data are available at https://github.com/THUDM/CaRR.

Long-form clinical videos are central to visual evidence-based decision-making, with growing importance for applications such as surgical robotics and related settings. However, current multimodal large language models typically process videos with passive sampling or weakly grounded inspection, which limits their ability to iteratively locate, verify, and justify predictions with temporally targeted evidence. To close this gap, we propose MedScope, a tool-using clinical video reasoning model that performs coarse-to-fine evidence seeking over long-form procedures. By interleaving intermediate reasoning with targeted tool calls and verification on retrieved observations, MedScope produces more accurate and trustworthy predictions that are explicitly grounded in temporally localized visual evidence. To address the lack of high-fidelity supervision, we build ClinVideoSuite, an evidence-centric, fine-grained clinical video suite. We then optimize MedScope with Grounding-Aware Group Relative Policy Optimization (GA-GRPO), which directly reinforces tool use with grounding-aligned rewards and evidence-weighted advantages. On full and fine-grained video understanding benchmarks, MedScope achieves state-of-the-art performance in both in-domain and out-of-domain evaluations. Our approach illuminates a path toward medical AI agents that can genuinely "think with videos" through tool-integrated reasoning. We will release our code, models, and data.

Industrial advertising question answering (QA) is a high-stakes task in which hallucinated content, particularly fabricated URLs, can lead to financial loss, compliance violations, and legal risk. Although Retrieval-Augmented Generation (RAG) is widely adopted, deploying it in production remains challenging because industrial knowledge is inherently relational, frequently updated, and insufficiently aligned with generation objectives. We propose a reinforced co-adaptation framework that jointly optimizes retrieval and generation through two components: (1) Graph-aware Retrieval (GraphRAG), which models entity-relation structure over a high-citation knowledge subgraph for multi-hop, domain-specific evidence selection; and (2) evidence-constrained reinforcement learning via Group Relative Policy Optimization (GRPO) with multi-dimensional rewards covering faithfulness, style compliance, safety, and URL validity. Experiments on an internal advertising QA dataset show consistent gains across expert-judged dimensions including accuracy, completeness, and safety, while reducing the hallucination rate by 72\%. A two-week online A/B test demonstrates a 28.6\% increase in like rate, a 46.2\% decrease in dislike rate, and a 92.7\% reduction in URL hallucination. The system has been running in production for over half a year and has served millions of QA interactions.

Large language models (LLM) often hallucinate, and while adding citations is a common solution, it is frequently insufficient for accountability as users struggle to verify how a cited source supports a generated claim. Existing methods are typically coarse-grained and fail to distinguish between direct quotes and complex reasoning. In this paper, we introduce Generation-time Fine-grained Provenance, a task where models must generate fluent answers while simultaneously producing structured, sentence-level provenance triples. To enable this, we present ReFInE (Relation-aware Fine-grained Interpretability & Evidence), a dataset featuring expert verified annotations that distinguish between Quotation, Compression, and Inference. Building on ReFInE, we propose GenProve, a framework that combines Supervised Fine-Tuning (SFT) with Group Relative Policy Optimization (GRPO). By optimizing a composite reward for answer fidelity and provenance correctness, GenProve significantly outperforms 14 strong LLMs in joint evaluation. Crucially, our analysis uncovers a reasoning gap where models excel at surface-level quotation but struggle significantly with inference-based provenance, suggesting that verifiable reasoning remains a frontier challenge distinct from surface-level citation.

Recent advances in large language models (LLMs) highlight the importance of post training techniques for improving reasoning and mathematical ability. Group Relative Policy Optimization (GRPO) has shown promise in this domain by combining group relative advantage estimation, PPO style clipping, and KL regularization. However, its complexity raises the question of whether all components are necessary for fostering reasoning behaviors. We conduct a systematic analysis of GRPO and identify two key findings: (1) incorporating negative feedback is essential training solely on actions above a baseline limits learning; and (2) PPO style constraints, such as policy ratio clipping, are not required to improve mathematical reasoning or performance. Building on these insights, we propose REINFORCE with Group Relative Advantage (RGRA), a simplified variant that retains group relative advantage estimation but removes PPO style clipping and policy ratio terms. Experiments across standard mathematical benchmarks indicate that RGRA has the potential to achieve stronger performance than GRPO. Our results suggest that simpler REINFORCE based approaches can effectively enhance reasoning in LLMs, offering a more transparent and efficient alternative to GRPO.

Group relative policy optimization (GRPO), a core methodological component of DeepSeekMath and DeepSeek-R1, has emerged as a cornerstone for scaling reasoning capabilities of large language models. Despite its widespread adoption and the proliferation of follow-up works, the theoretical properties of GRPO remain less studied. This paper provides a unified framework to understand GRPO through the lens of classical U-statistics. We demonstrate that the GRPO policy gradient is inherently a U-statistic, allowing us to characterize its mean squared error (MSE), derive the finite-sample error bound and asymptotic distribution of the suboptimality gap for its learned policy. Our findings reveal that GRPO is asymptotically equivalent to an oracle policy gradient algorithm -- one with access to a value function that quantifies the goodness of its learning policy at each training iteration -- and achieves asymptotically optimal performance within a broad class of policy gradient algorithms. Furthermore, we establish a universal scaling law that offers principled guidance for selecting the optimal group size. Empirical experiments further validate our theoretical findings, demonstrating that the optimal group size is universal, and verify the oracle property of GRPO.

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

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

Large Language Models (LLMs) have shown promise in solving complex mathematical problems, yet they still fall short of producing accurate and consistent solutions. Reinforcement Learning (RL) is a framework for aligning these models with task-specific rewards, improving overall quality and reliability. Group Relative Policy Optimization (GRPO) is an efficient, value-function-free alternative to Proximal Policy Optimization (PPO) that leverages group-relative reward normalization. We introduce Iterative Group Relative Policy Optimization (iGRPO), a two-stage extension of GRPO that adds dynamic self-conditioning through model-generated drafts. In Stage 1, iGRPO samples multiple exploratory drafts and selects the highest-reward draft using the same scalar reward signal used for optimization. In Stage 2, it appends this best draft to the original prompt and applies a GRPO-style update on draft-conditioned refinements, training the policy to improve beyond its strongest prior attempt. Under matched rollout budgets, iGRPO consistently outperforms GRPO across base models (e.g., Nemotron-H-8B-Base-8K and DeepSeek-R1 Distilled), validating its effectiveness on diverse reasoning benchmarks. Moreover, applying iGRPO to OpenReasoning-Nemotron-7B trained on AceReason-Math achieves new state-of-the-art results of 85.62\% and 79.64\% on AIME24 and AIME25, respectively. Ablations further show that the refinement wrapper generalizes beyond GRPO variants, benefits from a generative judge, and alters learning dynamics by delaying entropy collapse. These results underscore the potential of iterative, self-feedback-based RL for advancing verifiable mathematical reasoning.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as an important paradigm for unlocking reasoning capabilities in large language models, exemplified by the success of OpenAI o1 and DeepSeek-R1. Currently, Group Relative Policy Optimization (GRPO) stands as the dominant algorithm in this domain due to its stable training and critic-free efficiency. However, we argue that GRPO suffers from a structural limitation: it imposes a uniform, static trust region constraint across all samples. This design implicitly assumes signal homogeneity, a premise misaligned with the heterogeneous nature of outcome-driven learning, where advantage magnitudes and variances fluctuate significantly. Consequently, static constraints fail to fully exploit high-quality signals while insufficiently suppressing noise, often precipitating rapid entropy collapse. To address this, we propose Elastic Trust Regions (ETR), a dynamic mechanism that aligns optimization constraints with signal quality. ETR constructs a signal-aware landscape through dual-level elasticity: at the micro level, it scales clipping boundaries based on advantage magnitude to accelerate learning from high-confidence paths; at the macro level, it leverages group variance to implicitly allocate larger update budgets to tasks in the optimal learning zone. Extensive experiments on AIME and MATH benchmarks demonstrate that ETR consistently outperforms GRPO, achieving superior accuracy while effectively mitigating policy entropy degradation to ensure sustained exploration.

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

Reinforcement Learning has become a standard paradigm for aligning Large Language Models with human intent and task requirements. While Group Relative Policy Optimization offers an efficient, value-model-free alternative to Proximal Policy Optimization, adapting it to real-world multi-reward settings remains challenging. Standard scalarization practices, such as Reward Combination and Advantage Combination, suffer from significant drawbacks: Reward Combination frequently generates advantages with excessively large squared magnitudes that lead to training instability, while Advantage Combination relies on static hyperparameters and ignores cross-objective correlations. To address these limitations, we propose Dynamic Variance-adaptive Advantage Optimization (DVAO), which dynamically adjusts combination weights based on the empirical reward variance of each objective within a rollout group, effectively up-weighting objectives with a stronger learning signal while suppressing noisy ones. We mathematically prove that DVAO maintains bounded advantage magnitudes for stable training and introduces a self-adaptive cross-objective regularization mechanism. Extensive experiments on mathematical reasoning and tool-use benchmarks using Qwen3 and Qwen2.5 models demonstrate that DVAO significantly outperforms baseline methods, achieving a superior multi-objective Pareto frontier and robust training stability.

Group Relative Policy Optimization (GRPO) was introduced and used recently for promoting reasoning in LLMs under verifiable (binary) rewards. We show that the mean + variance calibration of these rewards induces a weighted contrastive loss in which the contrastive samples are synthetic data drawn from the previous policy. While GRPO was originally paired with clipping to keep updates near the old policy, we analyze variants that differ in reward normalization (mean-only vs mean + variance) and in how they regularize updates using KL divergence: either penalizing divergence from the previous model (mirror), penalizing divergence from a fixed reference model π_{ref}, or combining both forms of regularization. For each, the optimal policy π_n admits an explicit form in terms of the binary reward and the first and second order statistics of the reward under π_{n-1}, as well as the policies π_{n-1} and π_{ref}. Iterating results in a sequence {π_n} whose probability of success (PoS) obeys a simple recurrence that converges to a fixed point determined by the reference PoS and the regularization strength. We further show that this fixed point exceeds the reference, demonstrating that GRPO amplifies the policy's probability of success.

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

Group Relative Policy Optimization (GRPO) assigns a single scalar advantage to all tokens in a completion. For structured generations with explicit segments and objectives, this couples unrelated reward signals across segments, leading to objective interference and misattributed credit. We propose Blockwise Advantage Estimation, a family of GRPO-compatible methods that assigns each objective its own advantage and applies it only to the tokens in the corresponding text block, reducing reliance on hand-designed scalar rewards and scaling naturally to additional objectives. A key challenge is estimating advantages for later blocks whose rewards are conditioned on sampled prefixes; standard unbiased approaches require expensive nested rollouts from intermediate states. Concretely, we introduce an Outcome-Conditioned Baseline that approximates intermediate state values using only within-group statistics by stratifying samples according to a prefix-derived intermediate outcome. On math tasks with uncertainty estimation, our method mitigates reward interference, is competitive with a state-of-the-art reward-designed approach, and preserves test-time gains from confidence-weighted ensembling. More broadly, it provides a modular recipe for optimizing sequential objectives in structured generations without additional rollouts.

Group Relative Policy Optimization (GRPO) is widely used for reinforcement learning with verifiable rewards, but it often suffers from advantage collapse: when all rollouts in a group receive the same reward, the group yields zero relative advantage and thus no learning signal. For example, if a question is too hard for the reasoner, all sampled rollouts can be incorrect and receive zero reward. Recent work addresses this issue by adding hints or auxiliary scaffolds to such hard questions so that the reasoner produces mixed outcomes and recovers a non-zero update. However, existing hints are usually fixed rather than adapted to the current reasoner, and a hint that creates learning signal under the hinted input does not necessarily improve the no-hint policy used at test time. To this end, we propose Hint Learning for Reinforcement Learning (HiLL), a framework that jointly trains a hinter policy and a reasoner policy during RL. For each hard question, the hinter generates hints online conditioned on the current reasoner's incorrect rollout, allowing hint generation to adapt to the reasoner's evolving errors. We further introduce hint reliance, which measures how strongly correct hinted trajectories depend on the hint. We derive a transferability result showing that lower hint reliance implies stronger transfer from hinted success to no-hint success, and we use this result to define a transfer-weighted reward for training the hinter. Therefore, HiLL favors hints that not only recover informative GRPO groups, but also produce signals that are more likely to improve the original no-hint policy. Experiments across multiple benchmarks show that HiLL consistently outperforms GRPO and prior hint-based baselines, demonstrating the value of adaptive and transfer-aware hint learning for RL. The code is available at https://github.com/Andree-9/HiLL.

Reinforcement learning from verifiable rewards has significantly advanced the reasoning capabilities of large language models. However, Group Relative Policy Optimization (GRPO) typically assigns a uniform, sequence-level advantage to all tokens, thereby overlooking the intrinsic information heterogeneity along reasoning chains. We show that this coarse-grained credit assignment leads to premature entropy collapse and encourages the model to generate redundant, low-quality reasoning paths. Through systematic empirical analysis, we identify Critical Decision Pivots (CDPs): transient high-entropy states where the policy's trajectory is most sensitive to perturbations. These pivots represent the "forks in the road" where effective multi-path exploration is most crucial yet often suppressed by uniform advantage signals. Building on these insights, we propose Entropy-Regulated Policy Optimization (ERPO), which transitions the optimization focus from coarse sequences to fine-grained token dynamics. ERPO introduces three synergistic components: (i) Entropy-aware Gating, which adaptively amplifies exploration at CDPs to facilitate diverse path discovery; (ii) Bucket-based Implicit Normalization, which mitigates difficulty bias by aligning token progress windows; and (iii) Result-anchored Advantage Synthesis, which re-weights token-level signals via outcome-driven anchors. Extensive experiments on competitive mathematical benchmarks demonstrate that ERPO significantly outperforms GRPO. Notably, ERPO not only boosts reasoning accuracy but also yields significantly more concise and robust derivation paths, while achieving performance comparable to large models with orders of magnitude more parameters.

Reinforcement Learning with Verifiable Rewards (RLVR) has advanced the reasoning capabilities of Large Language Models (LLMs) by leveraging direct outcome verification instead of learned reward models. Building on this paradigm, Group Relative Policy Optimization (GRPO) eliminates the need for critic models but suffers from indiscriminate credit assignment for intermediate steps, which limits its ability to identify effective reasoning strategies and incurs overthinking. In this work, we introduce a model-free and verifiable process supervision via probing the model's belief in the correct answer throughout its reasoning trajectory. By segmenting the generation into discrete steps and tracking the conditional probability of the correct answer appended at each segment boundary, we efficiently compute interpretable segment-wise progress measurements to refine GRPO's trajectory-level feedback. This approach enables more targeted and sample-efficient policy updates, while avoiding the need for intermediate supervision derived from costly Monte Carlo rollouts or auxiliary models. Experiments on mathematical and general-domain benchmarks show consistent gains over GRPO across diverse models: up to 2.6-point accuracy improvements and 13.7% reasoning-length reductions on math tasks, and up to 2.4 points and 4% on general-domain tasks, demonstrating strong generalization.

Group-relative policy optimization has emerged as a key paradigm for training agentic large language models (LLMs) on multi-turn interactive tasks. However, most existing variants fail to distinguish advantages among successful trajectories even when these trajectories differ substantially in their interaction efficiency. For instance, circuitous successes are often assigned the identical outcome reward, causing advantage collapse and severe performance bottlenecks. To this end, we propose Group Planning-aware Policy Optimization (PlanPO), a simple yet effective RL method for learning generalizable planning abilities beyond task-specific high-quality behavior patterns. Specifically, PlanPO introduces coarse-to-fine advantage signals, which capture the relative differences in trajectory-level lengths and turn-level response lengths conditioned on successful trajectories sampled for the same task. Within the group-relative optimization structure, this enables agents to actively learn generalizable and deliberate behaviors spanning interaction planning and textual generation from high-quality rollouts, without degenerating into vanilla length minimization. Experimentally, PlanPO improves over GRPO by 27.2\% on average across the challenging multi-turn benchmarks ALFWorld, WebShop, and SciWorld, outperforming recent powerful baselines while incurring negligible additional training cost.

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

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

Group Relative Policy Optimization (GRPO) is one of the most widely adopted RLVR algorithms for post-training large language models on reasoning tasks. We first show that GRPO admits an equivalent discriminative reformulation, in which policy optimization maximizes the expected score gap between verified positive and negative rollouts. This reformulation reveals two objective-level limitations: likelihood-misaligned surrogate scores, in which clipped ratio-based scores are optimized rather than the sequence likelihoods that govern generation, and score-insensitive credit assignment, in which rollout-level credit does not reflect the current score gaps between positive and negative rollouts. To address these limitations, we propose ConSPO, a Contrastive Sequence-level Policy Optimization method that uses length-normalized sequence log-probabilities as rollout scores and contrasts verified positive rollouts against negative distractors within the same group. ConSPO optimizes a group-wise InfoNCE-style objective to adaptively strengthen updates for poorly separated positives and high-scoring negatives, together with a curriculum-scheduled margin that preserves separation pressure as training progresses. Experiments across diverse settings show that ConSPO outperforms strong baselines on challenging reasoning benchmarks. Code will be released upon paper acceptance.

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.

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

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

Group Relative Policy Optimization (GRPO) has become a standard reinforcement learning method for post-training language models. Recent work shows that GRPO can reduce the base model's reasoning capacity and underperform it in Pass@k when k is large, indicating reduced coverage of reasoning paths. We find that this reduction is associated with GRPO concentrating on responses that the base model already generates with high probability. We trace this concentration to two mechanisms in the GRPO update. At the response level, high-probability responses dominate the group gradient through repeated occurrence. At the token level, GRPO's importance ratio scales gradients, further reinforcing tokens that become more likely under the current policy. We propose ReCo, a reweighting method that addresses both effects. Response contributions are normalized by their expected occurrence within the rollout group, and the token-level importance ratio is replaced with a variance-based ratio that gives larger update scale to non-saturated decision points where alternative token choices remain plausible. Across Qwen2.5-Math-1.5B/7B and Llama-3.1-8B-Instruct on five mathematical reasoning benchmarks, ReCo improves Pass@k for large values of k and is comparable to GRPO for small values of k.

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.

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

Group Relative Policy Optimization (GRPO), a prominent algorithm within the Reinforcement Learning from Verifiable Rewards (RLVR) framework, has achieved strong results in improving the reasoning capabilities of large language models (LLMs). However, GRPO is prone to advantage collapse, a failure mode where homogeneous rewards within a group (e.g., all correct or all incorrect answers) yield near-zero advantages and vanishing gradients. To address this, we introduce the Advantage Collapse Rate (ACR), the first diagnostic metric quantifying the proportion of training batches with ineffective gradients. Across models from 0.5B to 14B parameters on mathematical reasoning benchmarks, we show that ACR strongly predicts training stagnation and final performance. We then propose Adaptive Virtual Sample Policy Optimization (AVSPO), a lightweight extension of GRPO that injects virtual reward samples, guided by real-time ACR monitoring, to enable learning from homogeneous groups without additional model rollouts. AVSPO reduces advantage collapse by 58-63% relative to GRPO and yields consistent accuracy gains of 4-6 percentage points across all model scales, while maintaining generalization on the evaluated out-of-domain task. Code and datasets are available at https://github.com/hexixiang/Advantage-Collapse-Rate.

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

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

While Group Relative Policy Optimization (GRPO) offers a powerful framework for LLM post-training, its effectiveness in open-ended domains like Machine Translation hinges on accurate intra-group ranking. We identify that standard Scalar Quality Metrics (SQM) fall short in this context; by evaluating candidates in isolation, they lack the comparative context necessary to distinguish fine-grained linguistic nuances. To address this, we introduce the Group Quality Metric (GQM) paradigm and instantiate it via the Group Relative Reward Model (GRRM). Unlike traditional independent scorers, GRRM processes the entire candidate group jointly, leveraging comparative analysis to rigorously resolve relative quality and adaptive granularity. Empirical evaluations confirm that GRRM achieves competitive ranking accuracy among all baselines. Building on this foundation, we integrate GRRM into the GRPO training loop to optimize the translation policy. Experimental results demonstrate that our framework not only improves general translation quality but also unlocks reasoning capabilities comparable to state-of-the-art reasoning models. We release codes, datasets, and model checkpoints at https://github.com/NJUNLP/GRRM.

Group Relative Policy Optimization (GRPO) has emerged as the de facto Reinforcement Learning (RL) objective driving recent advancements in Multimodal Large Language Models. However, extending this success to open-source multimodal generalist models remains heavily constrained by two primary challenges: the extreme variance in reward topologies across diverse visual tasks, and the inherent difficulty of balancing fine-grained perception with multi-step reasoning capabilities. To address these issues, we introduce Gaussian GRPO (G^2RPO), a novel RL training objective that replaces standard linear scaling with non-linear distributional matching. By mathematically forcing the advantage distribution of any given task to strictly converge to a standard normal distribution, N(0,1), G^2RPO theoretically ensures inter-task gradient equity, mitigates vulnerabilities to heavy-tail outliers, and offers symmetric update for positive and negative rewards. Leveraging the enhanced training stability provided by G^2RPO, we introduce two task-level shaping mechanisms to seamlessly balance perception and reasoning. First, response length shaping dynamically elicits extended reasoning chains for complex queries while enforce direct outputs to bolster visual grounding. Second, entropy shaping tightly bounds the model's exploration zone, effectively preventing both entropy collapse and entropy explosion. Integrating these methodologies, we present OpenVLThinkerV2, a highly robust, general-purpose multimodal model. Extensive evaluations across 18 diverse benchmarks demonstrate its superior performance over strong open-source and leading proprietary frontier models.

Group Relative Policy Optimization (GRPO) has been shown to be an effective algorithm when an accurate reward model is available. However, such a highly reliable reward model is not available in many real-world tasks. In this paper, we particularly focus on multi-objective settings, in which we identify that GRPO is vulnerable to reward hacking, optimizing only one of the objectives at the cost of the others. To address this issue, we propose MO-GRPO, an extension of GRPO with a simple normalization method to reweight the reward functions automatically according to the variances of their values. We first show analytically that MO-GRPO ensures that all reward functions contribute evenly to the loss function while preserving the order of preferences, eliminating the need for manual tuning of the reward functions' scales. Then, we evaluate MO-GRPO experimentally in four domains: (i) the multi-armed bandits problem, (ii) simulated control task (Mo-Gymnasium), (iii) machine translation tasks on the WMT benchmark (En-Ja, En-Zh), and (iv) instruction following task. MO-GRPO achieves stable learning by evenly distributing correlations among the components of rewards, outperforming GRPO, showing MO-GRPO to be a promising algorithm for multi-objective reinforcement learning problems.

Reinforcement learning has become a cornerstone for enhancing the reasoning capabilities of Large Language Models, where group-based approaches such as GRPO have emerged as efficient paradigms that optimize policies by leveraging intra-group performance differences. However, these methods typically rely on absolute numerical rewards, introducing intrinsic limitations. In verifiable tasks, identical group evaluations often result in sparse supervision, while in open-ended scenarios, the score range instability of reward models undermines advantage estimation based on group means. To address these limitations, we propose Reinforcement Learning with Relative Rewards (RLRR), a framework that shifts reward shaping from absolute scoring to relative ranking. Complementing this framework, we introduce the Ranking Reward Model, a listwise preference model tailored for group-based optimization to directly generate relative rankings. By transforming raw evaluations into robust relative signals, RLRR effectively mitigates signal sparsity and reward instability. Experimental results demonstrate that RLRR yields consistent performance improvements over standard group-based baselines across reasoning benchmarks and open-ended generation tasks.

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

We identify a new dimension for enhancing rollout diversity in Group Relative Policy Optimization (GRPO) for LLMs. While GRPO relies on diverse rollouts, prevailing strategies primarily increase diversity by injecting more token-level randomness, which may introduce step-wise noise and lead to incoherent trajectories. We uncover that smaller models within the same model family inherently exhibit higher policy-level diversity, indicated by their superior pass@k relative to larger counterparts as sample counts increase. Unlike token-level noise, this diversity is temporally correlated, preserves logical consistency, and provides structured exploration signals for gradient estimation. We thus propose S2L-PO (Small-to-Large Policy Optimization), a framework that leverages fixed small models as natural explorers to train larger models. To balance exploration and exploitation, we design a progressive annealing strategy that transitions from offline small-model rollouts to the large learner's own sampling. This shift elegantly avoids mid-training performance drops caused by the small model's capacity limits, achieving faster convergence and unlocking a higher performance ceiling. S2L-PO improves accuracy on diverse mathematical reasoning benchmarks (e.g., +8.8% on AIME 24 using a 1.7B explorer to guide the 8B model) while reducing rollout compute.

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.

Group Relative Policy Optimization (GRPO) has been a key driver of recent progress in reinforcement learning with verifiable rewards (RLVR) for large language models, but it is typically trained in a low-staleness, near-on-policy regime that incurs substantial system overhead. We ask a simple question: How off-policy can GRPO be? We show that GRPO-style algorithms can tolerate substantially larger rollout staleness than previously assumed, and propose Mu-GRPO, an RL training framework that organizes training into a small number (e.g., four) of large sequential generation-optimization stages. This design induces high rollout staleness while greatly reducing rollout-optimization switching overhead. To stabilize learning under stale data, Mu-GRPO combines relaxed clipping, which preserves useful stale-rollout gradients, with negative-advantage veto, which removes destabilizing post-trigger suffix updates in negative-advantage responses. Across five language models and multiple math reasoning benchmarks, Mu-GRPO matches or exceeds the performance of standard GRPO while achieving around 2x speedup in wall-clock training time, establishing a substantially improved performance-efficiency trade-off for LLM reinforcement learning.

Group Relative Policy Optimization (GRPO) has proven effective in RLVR by using outcome-based rewards. While fine-grained dense rewards can theoretically improve performance, we reveal that under practical sampling budgets, Monte Carlo estimation yields high-variance and sign-inconsistent advantages for early reasoning tokens, paradoxically underperforming outcome-only GRPO. We propose Skip-Connected Optimization (SKPO), which decomposes reasoning into upstream and downstream phases: upstream receives dense rewards from downstream Monte Carlo sampling with single-stream optimization; downstream maintains group-relative optimization, where a skip connection concatenates the upstream segment with the original problem, enabling the model to leverage helpful upstream reasoning while preserving the freedom to bypass flawed reasoning through direct problem access. Experiments demonstrate improvements of 3.91% and 6.17% relative gains over the strongest baselines on Qwen2.5-Math-7B and Llama-3.2-3B respectively across mathematical benchmarks and out-of-domain tasks including general reasoning and code generation. Further analysis reveals an implicit advantage: SKPO generates trajectories with higher intermediate-step quality even when matched for final correctness.

Group Relative Policy Optimization (GRPO) improves language-model reasoning by comparing verified rewards among multiple solution rollouts for each query. However, difficult training queries can yield only incorrect rollouts, leaving GRPO with no reward contrast or learning signal. Prior hint-based methods construct auxiliary hints from solution evidence and use them to re-solve failed queries, recovering learning signal. Yet the resulting trajectories are typically treated as ordinary solution trajectories despite being generated under an assisted condition unavailable at evaluation. We discover hinted reward shift: recovered reward contrast can concentrate policy updates on hinted trajectories, limiting improvement without hints. This also creates a trade-off: increasing hinted trajectories can accelerate early learning but intensify reward shift later. To address this problem, we propose HATCH (Hint-Annealed Self-Teaching), an online single-policy framework that learns from both generating and using its own hints to improve reasoning without assistance. To mitigate hinted reward shift, we introduce online weighting to anneal the contribution of hinted trajectories. However, learning to generate hints can conflict with improving query solving. We therefore use gradient projection to remove the opposing component of hint-generation updates. Together, these designs support self-improvement by enabling the policy to create learning opportunities for itself and turn them into stronger reasoning without hints. We evaluate our method on mathematical reasoning benchmarks and outperform state-of-the-art methods by 1.02 pp on Llama-3.2-1B-Instruct, 2.84 pp on Qwen3-1.7B, and 4.32 pp on Qwen3-8B.

Standard Reinforcement Learning with Verifiable Rewards (RLVR) training allocates a fixed rollout budget to every query, without regard for what each query's difficulty means for the current policy. This leads to two symmetric failure modes: easy queries produce near-zero advantage because the policy already solves them, while unsolvable queries produce no signal because the policy never solves them. Both regimes waste training FLOPs without contributing to a learning gradient. We introduce sorted Group Policy Optimization (sGPO), a compute-efficient strategy that trades a small budget of inference FLOPs for a large reduction in wasted training FLOPs. The key insight is that cheap inference compute can serve as a single offline proxy for query difficulty. By generating a small batch of parallel samples per query under the initial policy, we obtain a model-aware empirical success rate. This motivates setting the training rollout group size to the inverse of this success rate, a practical rule that maximizes sample efficiency by extracting the most advantage per generated rollout. This single profiling pass simultaneously drives data filtering (removing trivial queries and sub-sampling unsolvable ones), adaptive group size allocation, and curriculum construction (scheduling queries from easy to hard). sGPO matches or exceeds baseline performance while reducing total training compute by a factor of three, with the upfront inference profiling cost included.

Reinforcement Learning with Verifiable Rewards (RLVR) offers a robust mechanism for enhancing mathematical reasoning in large models. However, we identify a systematic lack of emphasis on more challenging questions in existing methods from both algorithmic and data perspectives, despite their importance for refining underdeveloped capabilities. Algorithmically, widely used Group Relative Policy Optimization (GRPO) suffers from an implicit imbalance where the magnitude of policy updates is lower for harder questions. Data-wise, augmentation approaches primarily rephrase questions to enhance diversity without systematically increasing intrinsic difficulty. To address these issues, we propose a two-dual MathForge framework to improve mathematical reasoning by targeting harder questions from both perspectives, which comprises a Difficulty-Aware Group Policy Optimization (DGPO) algorithm and a Multi-Aspect Question Reformulation (MQR) strategy. Specifically, DGPO first rectifies the implicit imbalance in GRPO via difficulty-balanced group advantage estimation, and further prioritizes harder questions by difficulty-aware question-level weighting. Meanwhile, MQR reformulates questions across multiple aspects to increase difficulty while maintaining the original gold answer. Overall, MathForge forms a synergistic loop: MQR expands the data frontier, and DGPO effectively learns from the augmented data. Extensive experiments show that MathForge significantly outperforms existing methods on various mathematical reasoning tasks. The code and augmented data are all available at https://github.com/AMAP-ML/MathForge.

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

Streaming video understanding requires models to repeatedly decide whether to respond or continue observing. Recently, Group Relative Policy Optimization (GRPO) has been applied to this setting, with existing approaches emphasizing reward design while retaining a single trajectory-level advantage across turns. Such shared credit can reinforce redundant replies after earlier successes and discourage useful follow-ups after earlier failures. We propose TurnWise, a turn-level GRPO framework that aligns learning with individual streaming decisions. TurnWise addresses the mismatch between trajectory-level feedback and turn-level interaction, promoting informative responses and reducing redundancy. Specifically, turn-level credit assignment uses silence-completed prefix scoring to construct group-relative advantages from each decision's remaining return, separating its learning signal from earlier rewards. Turn-mean policy optimization averages token losses within each turn and then across turns, giving response and waiting decisions equal weight regardless of output length. These complementary designs improve streaming policy learning without a learned critic or additional rollouts. Extensive experiments show our method outperforms prior RL approaches for streaming video understanding.

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

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.

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

Recent studies have demonstrated that Reinforcement Learning (RL), notably Group Relative Policy Optimization (GRPO), can intrinsically elicit and enhance the reasoning capabilities of Vision-Language Models (VLMs). However, despite the promise, the underlying mechanisms that drive the effectiveness of RL models as well as their limitations remain underexplored. In this paper, we highlight a fundamental behavioral distinction between RL and base models, where the former engages in deeper yet narrow reasoning, while base models, despite less refined along individual path, exhibit broader and more diverse thinking patterns. Through further analysis of training dynamics, we show that GRPO is prone to diversity collapse, causing models to prematurely converge to a limited subset of reasoning strategies while discarding the majority of potential alternatives, leading to local optima and poor scalability. To address this, we propose Multi-Group Policy Optimization (MUPO), a simple yet effective approach designed to incentivize divergent thinking across multiple solutions, and demonstrate its effectiveness on established benchmarks. Project page: https://xytian1008.github.io/MUPO/

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

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

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

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

Group Relative Policy Optimisation (GRPO) enhances large language models by estimating advantages across a group of sampled trajectories. However, mapping these trajectory-level advantages to policy updates requires aggregating token-level probabilities within each sequence. Relying on a fixed aggregation mechanism for this step fundamentally limits the algorithm's adaptability. Empirically, we observe a critical trade-off: certain fixed aggregations frequently suffer from training collapse, while others fail to yield satisfactory performance. To resolve this, we propose HölderPO, a generalised policy optimisation framework unifying token-level probability aggregation via the Hölder mean. By explicitly modulating the parameter p, our framework provides continuous control over the trade-off between gradient concentration and variance bounds. Theoretically, we prove that a larger p concentrates the gradient to amplify sparse learning signals, whereas a smaller p strictly bounds gradient variance. Because no static configuration can universally resolve this concentration-stability trade-off, we instantiate the framework with a dynamic annealing algorithm that progressively schedules p across the training lifecycle. Extensive evaluations demonstrate superior stability and convergence over existing baselines. Specifically, our approach achieves a state-of-the-art average accuracy of 54.9% across multiple mathematical benchmarks, yielding a substantial 7.2% relative gain over standard GRPO and secures an exceptional 93.8% success rate on ALFWorld.

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

Group Relative Policy Optimization (GRPO) has recently emerged as a practical recipe for aligning large language models with verifiable objectives. However, under sparse terminal rewards, GRPO often stalls because rollouts within a group frequently receive identical rewards, causing relative advantages to collapse and updates to vanish. We propose self-hint aligned GRPO with privileged supervision (SAGE), an on-policy reinforcement learning framework that injects privileged hints during training to reshape the rollout distribution under the same terminal verifier reward. For each prompt x, the model samples a compact hint h (e.g., a plan or decomposition) and then generates a solution τ conditioned on (x,h). Crucially, the task reward R(x,τ) is unchanged; hints only increase within-group outcome diversity under finite sampling, preventing GRPO advantages from collapsing under sparse rewards. At test time, we set h=varnothing and deploy the no-hint policy without any privileged information. Moreover, sampling diverse self-hints serves as an adaptive curriculum that tracks the learner's bottlenecks more effectively than fixed hints from an initial policy or a stronger external model. Experiments over 6 benchmarks with 3 LLMs show that SAGE consistently outperforms GRPO, on average +2.0 on Llama-3.2-3B-Instruct, +1.2 on Qwen2.5-7B-Instruct and +1.3 on Qwen3-4B-Instruct. The code is available at https://github.com/BaohaoLiao/SAGE.

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

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

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

Chain-of-thought (CoT) reasoning improves large language model performance on complex tasks, but often produces excessively long and inefficient reasoning traces. Existing methods shorten CoTs using length penalties or global entropy reduction, implicitly assuming that low uncertainty is desirable throughout reasoning. We show instead that reasoning efficiency is governed by the trajectory of uncertainty. CoTs with dominant downward entropy trends are substantially shorter. Motivated by this insight, we propose Entropy Trend Reward (ETR), a trajectory-aware objective that encourages progressive uncertainty reduction while allowing limited local exploration. We integrate ETR into Group Relative Policy Optimization (GRPO) and evaluate it across multiple reasoning models and challenging benchmarks. ETR consistently achieves a superior accuracy-efficiency tradeoff, improving DeepSeek-R1-Distill-7B by 9.9% in accuracy while reducing CoT length by 67% across four benchmarks. Code is available at https://github.com/Xuan1030/ETR

Group Relative Policy Optimization (GRPO) has demonstrated remarkable success in aligning text-to-image (T2I) flow models with human preferences. However, we have identified that the learning loop of current flow-based GRPO is fundamentally decoupled from the learner's current capability, suffering from critical blind spots at both prompt selection and advantage estimation: (i) Existing methods sample prompts randomly, overlooking the substantial impact of data selection on reinforcement learning (RL) efficacy--a factor proven crucial in GRPO for large language models; (ii) They evaluate sample quality solely relying on intra-group statistics, lacking a global perspective to accurately measure true policy improvement. To address these issues, we propose Adaptive GRPO (AdaGRPO), a novel capability-aware RL algorithm tailored for flow models. Specifically, AdaGRPO consists of two principal components: (i) Online Curriculum Filtering Strategy: Dynamically tracks the model's proficiency and adaptively selects prompts that best match its current learning boundary; (ii) Cross-Level Advantage Fusion: Synergistically integrates fine-grained intra-group advantages with macro-level global advantages, providing a comprehensive and unbiased policy evaluation. As a lightweight, plug-and-play module, AdaGRPO can be seamlessly integrated with existing frameworks such as Flow-GRPO, DanceGRPO, and Flow-CPS. Extensive experiments demonstrate that AdaGRPO consistently drives performance gains while significantly stabilizes GRPO training for flow models.

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

Reinforcement learning (RL) plays a central role in large language model (LLM) post-training. Among existing approaches, Group Relative Policy Optimization (GRPO) is widely used, especially for RL with verifiable rewards (RLVR) fine-tuning. In GRPO, each query prompts the LLM to generate a group of rollouts with a fixed group size N. When all rollouts in a group share the same outcome, either all correct or all incorrect, the group-normalized advantages become zero, yielding no gradient signal and wasting fine-tuning compute. We introduce Adaptive Efficient Rollout Optimization (AERO), an enhancement of GRPO. AERO uses an adaptive rollout strategy, applies selective rejection to strategically prune rollouts, and maintains a Bayesian posterior to prevent zero-advantage dead zones. Across three model configurations (Qwen2.5-Math-1.5B, Qwen2.5-7B, and Qwen2.5-7B-Instruct), AERO improves compute efficiency without sacrificing performance. Under the same total rollout budget, AERO reduces total training compute by about 48% while shortening wall-clock time per step by about 45% on average. Despite the substantial reduction in compute, AERO matches or improves Pass@8 and Avg@8 over GRPO, demonstrating a practical, scalable, and compute-efficient strategy for RL-based LLM alignment.

The success of Large Language Models in mathematical reasoning relies heavily on the generation of diverse and valid solution paths during the rollout phase. However, current rollout techniques face a fundamental trade-off: token-level sampling often yields redundant trajectories that differ only in rephrasing, while embedding-level methods utilizing random noise frequently disrupt semantic consistency. To resolve this, we introduce N-GRPO, a novel exploration strategy integrated into the Group Relative Policy Optimization (GRPO) framework. Rather than relying on token-level sampling or native embedding-level noise, our approach leverages Semantic Neighbor Mixing. This mechanism dynamically constructs input representations by mixing the embeddings of an anchor token and its nearest semantic neighbors, thereby injecting diversity while strictly adhering to the local semantic manifold. Experimental evaluations on the DeepSeek-R1-Distill-Qwen models across different sizes show that N-GRPO not only achieves consistent improvements over strong baselines on math reasoning benchmarks but also exhibits robust generalization capabilities on out-of-distribution tasks.

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.

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

Group Relative Policy Optimization (GRPO) is effective when the current policy already samples useful reasoning trajectories, but it stalls on hard prompts whose correct solution modes lie outside the student's on-policy support. We propose TREK (Teacher-Routed Exploration via Forward KL), a simple staged procedure that uses distillation not for imitation but for exploration support expansion. A key advantage of TREK is its generality: because it only consumes verified output trajectories, it can use an external black-box teacher, a white-box teacher, or the same model given additional inference-time context, and it can efficiently identify which hard-prompt samples are most worth consolidating even when teacher internals are unavailable. TREK first identifies prompts where the unaided student has very low pass rate, queries a proposal source to produce verified candidate solutions, keeps the top-r proposals ranked by current student likelihood, applies a short forward-KL phase to pull those verified modes into the student's support, and then returns to standard on-policy GRPO refinement. On mathematical reasoning, TREK with DeepSeek-V4 proposals improves Qwen3 models across all tested scales on AIME 2024 and AIME 2025; for Qwen3-8B, it improves AIME 2025 from 36.9 to 40.3 and AIME 2024 from 47.9 to 51.1 (avg@16), while the self-context variant reaches 38.5 and 49.6 without an external teacher. On agentic tasks, TREK raises ALFWorld success rate from 75.8 to 82.8 and ScienceWorld success rate from 12.5 to 26.7; notably, on the hardest task types, TREK achieves high success rates early in training while unaided GRPO requires substantially more optimization steps to reach comparable levels.

Optimizing communication topology is fundamental to the efficiency and effectiveness of Large Language Model (LLM)-based Multi-Agent Systems (MAS). While recent approaches utilize reinforcement learning to dynamically construct task-specific graphs, they typically rely on single-sample policy gradients with absolute rewards (e.g., binary correctness). This paradigm suffers from severe gradient variance and the credit assignment problem: simple queries yield non-informative positive rewards for suboptimal structures, while difficult queries often result in failures that provide no learning signal. To address these challenges, we propose Graph-GRPO, a novel topology optimization framework that integrates Group Relative Policy Optimization. Instead of evaluating a single topology in isolation, Graph-GRPO samples a group of diverse communication graphs for each query and computes the advantage of specific edges based on their relative performance within the group. By normalizing rewards across the sampled group, our method effectively mitigates the noise derived from task difficulty variance and enables fine-grained credit assignment. Extensive experiments on reasoning and code generation benchmarks demonstrate that Graph-GRPO significantly outperforms state-of-the-art baselines, achieving superior training stability and identifying critical communication pathways previously obscured by reward noise.

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

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

LLM-based search agents are increasingly trained on entity-centric synthetic data to solve complex, knowledge-intensive tasks. However, prevailing training methods like Group Relative Policy Optimization (GRPO) discard this rich entity information, relying instead on sparse, outcome-based rewards. This critical limitation renders them unable to distinguish informative "near-miss" samples-those with substantially correct reasoning but a flawed final answer-from complete failures, thus discarding valuable learning signals. We address this by leveraging the very entities discarded during training. Our empirical analysis reveals a strong positive correlation between the number of ground-truth entities identified during an agent's reasoning process and final answer accuracy. Building on this insight, we introduce Entity-aware Group Relative Policy Optimization (E-GRPO), a novel framework that formulates a dense entity-aware reward function. E-GRPO assigns partial rewards to incorrect samples proportional to their entity match rate, enabling the model to effectively learn from these "near-misses". Experiments on diverse question-answering (QA) and deep research benchmarks show that E-GRPO consistently and significantly outperforms the GRPO baseline. Furthermore, our analysis reveals that E-GRPO not only achieves superior accuracy but also induces more efficient reasoning policies that require fewer tool calls, demonstrating a more effective and sample-efficient approach to aligning search agents.

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

Standard reinforcement learning from human feedback (RLHF) trains a reward model on pairwise preference data and then uses it for policy optimization. However, while reward models are optimized to capture relative preferences, existing policy optimization techniques rely on absolute reward magnitudes during training. In settings where the rewards are non-verifiable such as summarization, instruction following, and chat completion, this misalignment often leads to suboptimal performance. We introduce Group Ordinal Policy Optimization (GOPO), a policy optimization method that uses only the ranking of the rewards and discards their magnitudes. Our rank-based transformation of rewards provides several gains, compared to Group Relative Policy Optimization (GRPO), in settings with non-verifiable rewards: (1) consistently higher training/validation reward trajectories, (2) improved LLM-as-judge evaluations across most intermediate training steps, and (3) reaching a policy of comparable quality in substantially less training steps than GRPO. We demonstrate consistent improvements across a range of tasks and model sizes.

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

Latent reasoning offers a more efficient alternative to explicit reasoning by compressing intermediate reasoning into continuous representations and substantially shortening reasoning chains. However, existing latent reasoning methods mainly focus on supervised learning, and reinforcement learning in latent space remains highly unstable. We study this problem through the lens of Group Relative Policy Optimization (GRPO), and show that directly adapting GRPO to latent reasoning is fundamentally non-trivial: latent reasoning changes both the probability density and the sampling mechanism, causing three coupled bottlenecks: absence of intrinsic latent manifolds, where unconstrained exploration pushes rollouts off the valid latent manifold; exploration-optimization misalignment, where trajectory-level rewards can induce incorrect token-level updates; and latent mixture non-closure, where jointly reinforcing multiple correct latent paths can produce an invalid averaged state. To address them, we propose Latent-GRPO, which combines invalid-sample advantage masking, one-sided noise sampling, and optimal correct-path first-token selection. Across four low-difficulty benchmarks (e.g., GSM8K-Aug) and four high-difficulty benchmarks (e.g., AIME), Latent-GRPO improves over its latent initialization by 7.86 Pass@1 points on low-difficulty tasks and surpasses explicit GRPO by 4.27 points on high-difficulty tasks while using 3--4times shorter reasoning chains. It also achieves stronger pass@k performance under Gumbel sampling. These results establish Latent-GRPO as an effective approach for stable and efficient latent reasoning.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising approach to improve the reasoning abilities of Large Language Models (LLMs). Among RLVR algorithms, Group Relative Policy Optimization (GRPO) and its variants have demonstrated strong performance and high training efficiency. However, GRPO-style objectives exhibit two issues on high accuracy prompts including mastered prompts (rollout accuracy =1) and majority-correct prompts (rollout accuracy in (0.5,1)). For mastered prompts, group-relative advantages vanish, yielding no training signal and unconstrained policy drift that can cause forgetting. For majority-correct prompts, the induced query weight shrinks as accuracy increases, weakening consolidation from partial correctness to mastery. To alleviate this, we propose Mastery-Consolidated Policy Optimization (MCPO), which introduces (i) a hinge-KL regularizer applied exclusively to mastered prompts to bound harmful policy drift between successive gradient steps, and (ii) a weighting mechanism that prioritizes majority-correct prompts to better allocate optimization effort. Extensive experiments across three mathematical benchmarks demonstrate that MCPO consistently improves pass@1 performance. Counter-intuitively, rather than restricting exploration, MCPO boosts pass@k metrics, indicating that mastery consolidation further catalyzes solution diversity.

Agentic reinforcement learning (RL) has become a critical stage in the post-training of large language models. Existing critic-free, group-relative methods estimate policy advantages from multiple rollouts, avoiding the substantial memory overhead of conventional proximal policy optimization (PPO) and achieving strong performance on long-horizon interactive tasks. Despite their success, recent studies revealed three limitations: (1) Lack explicit value generalization and effective temporal credit assignment; (2) Suffer from potential advantage collapse in long-horizon complex tasks; (3) Require a costly trade-off between sampling budget and policy performance. In this work, we propose Single-rollout Autoregressive Policy Optimization (SAPO), a low-memory and compute-efficient framework in which the policy and value functions share a single autoregressive backbone. SAPO exploits the autoregressive structure of LLMs to produce policy and value predictions at distinct causal boundaries with shared parameters, while independently optimizing the PPO objectives and auxiliary on-policy SARSA objectives. To robustly estimate the contribution of each turn, we further introduce a trajectory-level generalized advantage estimator that combines lambda-returns with batch normalization. Experiments across ALFWorld and WebShop with Qwen2.5-1.5B/7B show that SAPO trains stably and outperforms PPO and GRPO by mean +15.1 and +12.1 percentage points, respectively, while eliminating the memory cost of a separate critic model and reducing per-iteration runtime by 33.2% over PPO.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as an indispensable paradigm for enhancing reasoning in Large Language Models (LLMs). However, standard policy optimization methods, such as Group Relative Policy Optimization (GRPO), often converge to low-entropy policies, leading to severe mode collapse and limited output diversity. We analyze this issue from the perspective of sampling probability dynamics, identifying that the standard objective disproportionately reinforces the highest-likelihood paths, thereby suppressing valid alternative reasoning chains. To address this, we propose a novel Advantage Re-weighting Mechanism (ARM) designed to equilibrate the confidence levels across all correct responses. By incorporating Prompt Perplexity and Answer Confidence into the advantage estimation, our method dynamically reshapes the reward signal to attenuate the gradient updates of over-confident reasoning paths, while redistributing probability mass toward under-explored correct solutions. Empirical results demonstrate that our approach significantly enhances generative diversity and response entropy while maintaining competitive accuracy, effectively achieving a superior trade-off between exploration and exploitation in reasoning tasks. Empirical results on Qwen2.5 and DeepSeek models across mathematical and coding benchmarks show that ProGRPO significantly mitigates entropy collapse. Specifically, on Qwen2.5-7B, our method outperforms GRPO by 5.7% in Pass@1 and, notably, by 13.9% in Pass@32, highlighting its superior capability in generating diverse correct reasoning paths.

Policy gradient methods rely on a baseline to measure the relative advantage of an action, ensuring the model reinforces behaviors that outperform its current average capability. In the training of Large Language Models (LLMs) using Actor-Critic methods (e.g., PPO), this baseline is typically estimated by a Value Model (Critic) often as large as the policy model itself. However, as the policy continuously evolves, the value model requires expensive, synchronous incremental training to accurately track the shifting capabilities of the policy. To avoid this overhead, Group Relative Policy Optimization (GRPO) eliminates the coupled value model by using the average reward of a group of rollouts as the baseline; yet, this approach necessitates extensive sampling to maintain estimation stability. In this paper, we propose V_0, a Generalist Value Model capable of estimating the expected performance of any model on unseen prompts without requiring parameter updates. We reframe value estimation by treating the policy's dynamic capability as an explicit context input; specifically, we leverage a history of instruction-performance pairs to dynamically profile the model, departing from the traditional paradigm that relies on parameter fitting to perceive capability shifts. Focusing on value estimation at State Zero (i.e., the initial prompt, hence V_0), our model serves as a critical resource scheduler. During GRPO training, V_0 predicts success rates prior to rollout, allowing for efficient sampling budget allocation; during deployment, it functions as a router, dispatching instructions to the most cost-effective and suitable model. Empirical results demonstrate that V_0 significantly outperforms heuristic budget allocation and achieves a Pareto-optimal trade-off between performance and cost in LLM routing tasks.

Automated fact-checking remains a challenge for Large Language Models (LLMs) due to "query brittleness" in traditional retrieval systems. We propose DeLIVeR (Decomposed Learning for Information-grounded Veracity Recognition), a framework that treats evidence retrieval as a reinforced strategic exploration task. DeLIVeR utilizes a Planner LLM to decompose complex claims into targeted question sets, which are used to traverse structured Knowledge Graphs (KGs) for high-precision evidence. We optimize the Planner's policy using Group Relative Policy Optimization (GRPO) with a reward system prioritizing structural diversity and verdict accuracy. Our evaluation on LIAR, FEVER, and PolitiFact shows that DeLIVeR significantly outperforms state-of-the-art baselines. Using Qwen2.5-7B, our framework achieved peak F1-scores of 83.73, 84.57, and 79.70 respectively, representing a 10-15% improvement over HippoRAG2. By shifting to a reinforced question-planning strategy, DeLIVeR effectively bridges multi-hop reasoning gaps and provides an auditable, transparent path for verifiable misinformation detection.

Vision-Language-Action (VLA) models are advancing autonomous driving by replacing modular pipelines with unified end-to-end architectures. However, current VLAs face two expensive requirements: (1) massive dataset collection, and (2) dense reasoning annotations. In this work, we address both challenges with NORD (No Reasoning for Driving). Compared to existing VLAs, NORD achieves competitive performance while being fine-tuned on <60% of the data and no reasoning annotations, resulting in 3x fewer tokens. We identify that standard Group Relative Policy Optimization (GRPO) fails to yield significant improvements when applied to policies trained on such small, reasoning-free datasets. We show that this limitation stems from difficulty bias, which disproportionately penalizes reward signals from scenarios that produce high-variance rollouts within GRPO. NORD overcomes this by incorporating Dr. GRPO, a recent algorithm designed to mitigate difficulty bias in LLMs. As a result, NORD achieves competitive performance on Waymo and NAVSIM with a fraction of the training data and no reasoning overhead, enabling more efficient autonomous systems. Website: https://nord-vla-ai.github.io/

Reinforcement Learning (RL) enhances LLM reasoning, yet a paradox emerges as models scale: strong base models saturate standard benchmarks (e.g., MATH), yielding correct but homogeneous solutions. In such environments, the lack of failure cases causes the advantage signal in group-relative algorithms (e.g., GRPO) to vanish, driving policies into mode collapse. To address this, we propose Constrained Uniform Top-K Sampling (CUTS), a parameter-free decoding strategy enforcing structure-preserving exploration. Unlike standard sampling that follows model biases, CUTS flattens the local optimization landscape by sampling uniformly from constrained high-confidence candidates. We integrate this into Mixed-CUTS, a training framework synergizing exploitative and exploratory rollouts to amplify intra-group advantage variance. Experiments on Qwen3 models demonstrate that our approach prevents policy degeneration and significantly boosts out-of-domain generalization. Notably, Mixed-CUTS improves Pass@1 accuracy on the challenging AIME25 benchmark by up to 15.1% over standard GRPO, validating that maintaining diversity within the semantic manifold is critical for rigorous reasoning.

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

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.

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

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

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

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

Group-based Reinforcement Learning (RL) has significantly enhanced Large Language Models (LLMs) in agentic scenarios. To achieve finer-grained policy updates, recent agentic RL frameworks have shifted from trajectory-level to step-level training. However, long-horizon agentic RL suffers from severe reward sparsity and delay, as feedback is often deferred for dozens of interaction steps. While existing step-level frameworks refine training granularity, their credit assignment remains coarse-grained and still treats agent exploration as isolated, linear trajectories. This oversimplified perspective ignores the inherent graph structure of state transitions, leading to high-variance state-value estimation and myopic, localized credit assignment. To overcome these critical bottlenecks, we propose Group-Graph Policy Optimization (G2PO), a novel group-based RL algorithm tailored for multi-turn agentic tasks. G2PO explicitly transforms linear interaction trajectories into a global state-transition graph. By aggregating identical observations across different trajectories, we introduce group-aggregation state-value estimation that reduces sampling variance and trajectory-dependent bias. Furthermore, we redefine agent actions as transitions between state nodes and propose an edge-centric advantage estimation strategy. By globally standardizing Temporal Difference (TD) errors across the entire graph, G2PO explicitly identifies and prioritizes critical transitions that drive absolute task progress. Extensive experiments on representative long-horizon benchmarks-WebShop, ALFWorld, and AppWorld-demonstrate that G2PO substantially outperforms state-of-the-art prompt-based and RL baselines, achieving remarkable success rate improvements of up to 22.2% over GRPO.

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

While scaling individual Large Language Models (LLMs) has delivered remarkable progress, the next frontier lies in scaling collaboration through multi-agent systems (MAS). However, purely autonomous MAS remain ''closed-world'' systems, constrained by the static knowledge horizon of pre-trained models. This limitation makes them brittle on tasks requiring knowledge beyond training data, often leading to collective failure under novel challenges. To address this, we propose the Human-In-the-Loop Multi-Agent Collaboration (HILA) framework, a principled paradigm for human--agent collaboration. HILA trains agents to learn a metacognitive policy that governs when to solve problems autonomously and when to defer to a human expert. To operationalize this policy, we introduce Dual-Loop Policy Optimization, which disentangles immediate decision-making from long-term capability growth. The inner loop applies Group Relative Policy Optimization (GRPO) with a cost-aware reward to optimize deferral decisions, while the outer loop implements continual learning, transforming expert feedback into high-quality supervised signals that strengthen the agent's reasoning ability. Experiments on challenging mathematical and problem-solving benchmarks show that HILA, equipped with Dual-Loop Policy Optimization, consistently outperforms advanced MAS, establishing a principled foundation for collaborative and continually improving agentic systems.

Group-relative policy optimization methods train language models by generating multiple rollouts per prompt and normalizing rewards with a shared mean reward baseline. In resource-constrained settings where the rollout budget is small, accuracy often degrades. We find that noise in the shared baseline induces advantage sign flips, where some rollouts receive an incorrect advantage sign, and the update direction is reversed. To address this, we propose Median-Centered Group Relative Policy Optimization (MC-GRPO), a simple and effective solution for small-rollout training. Our main idea is to replace the mean baseline with a median baseline: the median is far less sensitive to outlier rewards than the mean, mitigating the sign flips under small rollout size (G). We generate one additional rollout for median reference (G+1), and compute advantages by using the group median. With an odd-sized group, exactly one completion is the median and receives zero advantage, we exclude this pivot rollout from backpropagation so the number of gradient-contributing samples per prompt remains G, preserving the core update cost of standard G-rollout training. Across various GRPO-family methods and a wide range of models and scales, this median-centered training consistently improves stability and final accuracy in the low-rollout regime, reducing the gap between G=2 and G=8 to within 1%. Code is available at https://github.com/lotusroot-kim/MC-GRPO

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.

Reinforcement Learning with Verifiable Rewards (RLVR) offers a promising framework for optimizing large language models in reasoning tasks. However, existing RLVR algorithms focus on different granularities, and each has complementary strengths and limitations. Group Relative Policy Optimization (GRPO) updates the policy with token-level importance ratios, which preserves fine-grained credit assignment but often suffers from high variance and instability. In contrast, Group Sequence Policy Optimization (GSPO) applies single sequence-level importance ratios across all tokens in a response that better matches sequence-level rewards, but sacrifices token-wise credit assignment. In this paper, we propose Dynamic Hybrid Policy Optimization (DHPO) to bridge GRPO and GSPO within a single clipped surrogate objective. DHPO combines token-level and sequence-level importance ratios using weighting mechanisms. We explore two variants of the mixing mechanism, including an averaged mixing and an entropy-guided mixing. To further stabilize training, we employ a branch-specific clipping strategy that constrains token-level and sequence-level ratios within separate trust regions before mixing, preventing outliers in either branch from dominating the update. Across seven challenging mathematical reasoning benchmarks, experiments on both dense and MoE models from the Qwen3 series show that DHPO consistently outperforms GRPO and GSPO. We will release our code upon acceptance of this paper.

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.

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

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.

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

Recent progress in Large Language Model (LLM) reasoning is increasingly driven by the refinement of post-training loss functions and alignment strategies. However, standard Reinforcement Learning (RL) paradigms like Group Relative Policy Optimization (GRPO) remain constrained by static uniformity: uniform prompt sampling and a fixed number of rollouts per prompt. For heterogeneous, heavy-tailed reasoning data, this creates structural inefficiencies that waste compute on already-solved patterns while under-training the long tail of hard problems. To address this, we propose Multi-Adversary Group Distributionally Robust Optimization (GDRO), an optimization-first framework that moves beyond uniform reasoning models by dynamically adapting the training distribution. We introduce an Online Difficulty Classifier that partitions prompts into dynamic pass@k difficulty groups. We then propose two independent GDRO games for post-training: (1) Prompt-GDRO, which employs an EMA-debiased multiplicative-weights bandit sampler to target the intensive difficulty margin and upweight persistently hard groups without frequency bias; and (2) Rollout-GDRO, which uses a shadow-price controller to reallocate rollouts across groups, maximizing gradient variance reduction on hard tasks under a fixed mean budget (compute-neutral). We provide no-regret guarantees for both controllers and additionally a variance-proxy analysis motivating a square-root optimal rollout allocation for Rollout-GDRO. We validate our framework on the DAPO 14.1k dataset using Qwen3-Base models. Prompt-GDRO and Rollout-GDRO achieve average relative gains of +10.6% and +10.1%, respectively, in pass@8 accuracy across 1.7B, 4B, and 8B scales compared to the GRPO baseline. Qualitative analysis shows an emergent curriculum: the adversaries shift resources to the evolving reasoning frontier, enhancing the reasoning model's performance.

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

Reinforcement learning (RL) for code agents often uses executable tests to provide binary rewards. With these rewards, Group Relative Policy Optimization (GRPO) assigns identical advantages to test-passing trajectories within each rollout group, overlooking differences in implementation quality and adherence to task requirements. This leaves the policy without a learning signal that favors clean, targeted implementations over those containing unnecessary or out-of-scope changes. We introduce GAGAR, a framework for quality-aware credit redistribution in code agent RL. Built on dynamic sampling that retains groups containing both passing and failing trajectories, GAGAR places all trajectories from each group in a shared workspace, where an SFT-trained agentic grader jointly inspects them and ranks the test-passing candidates. Based on this ranking, we downweight lower-ranked trajectories and proportionally rescale the advantages of all test-passing trajectories to restore their original sum. This sum-preserving redistribution retains the relative weights established by quality-based downweighting while shifting credit toward higher-quality implementations. We evaluate GAGAR at industrial scale using pre-RL SFT checkpoints of MiMo-V2.6-Flash (310B total parameters) and MiMo-V2.6-Pro (1.02T total parameters). Controlled code-only Flash experiments show improved code agent performance, reduced trajectory-length growth, and more stable training. We further apply GAGAR in large-scale mixed-task RL with both Flash and Pro. Our results support combining test-based verification with groupwise agentic grading to improve the quality and stability of code agent RL.

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

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising paradigm for post-training reasoning models. However, group-based methods such as Group Relative Policy Optimization (GRPO) face a critical dilemma in sparse-reward settings: pure Reinforcement Learning (RL) suffers from advantage collapse and high-variance gradient estimation, while mixed-policy optimization introduces persistent distributional bias. To resolve this dilemma, we introduce Hindsight-Anchored Policy Optimization (HAPO). HAPO employs the Synthetic Success Injection (SSI) operator, a hindsight mechanism that selectively anchors optimization to teacher demonstrations during failure. This injection is governed by a Thompson sampling-inspired gating mechanism, creating an autonomous, self-paced curriculum. Theoretically, we demonstrate that HAPO achieves asymptotic consistency: by naturally annealing the teacher signal as the policy improves, HAPO recovers the unbiased on-policy gradient. This ensures off-policy guidance acts as a temporary scaffold rather than a persistent ceiling, enabling the model to surpass the limitations of static teacher forcing.

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

Large reasoning models (LRMs) aim to solve diverse and complex problems through structured reasoning. Recent advances in group-based policy optimization methods have shown promise in enabling stable advantage estimation without reliance on process-level annotations. However, these methods rely on advantage gaps induced by high-quality samples within the same batch, which makes the training process fragile and inefficient when intra-group advantages collapse under challenging tasks. To address these problems, we propose a reinforcement learning mechanism named \textbf{R^3} that along three directions: (1) a cross-context \underline{\textbf{R}eplay} strategy that maintains the intra-group advantage by recalling valuable examples from historical trajectories of the same query, (2) an in-context self-\underline{\textbf{R}eflection} mechanism enabling models to refine outputs by leveraging past failures, and (3) a structural entropy \underline{\textbf{R}anking reward}, which assigns relative rewards to truncated or failed samples by ranking responses based on token-level entropy patterns, capturing both local exploration and global stability. We implement our method on Deepseek-R1-Distill-Qwen-1.5B and train it on the DeepscaleR-40k in the math domain. Experiments demonstrate our method achieves SoTA performance on several math benchmarks, representing significant improvements and fewer reasoning tokens over the base models. Code and model will be released.

Group Relative Policy Optimization (GRPO) is widely used to train reasoning language models, where it computes advantages by centering and normalizing rewards across rollouts of the same prompt. For multiple rewards, GRPO sums the reward components and normalizes the total reward by its within-group standard deviation. The corresponding variance equals the sum of all pairwise reward covariances. For a fixed centered reward, larger aggregate covariance produces smaller advantages, and vice versa, allowing update magnitudes to adapt to reward dependence. However, correlated rewards with large scales can dominate this normalization and suppress signals from smaller-scale rewards. We propose Correlation-Normalized GRPO (CorrGRPO), which normalizes pairwise covariances into Pearson correlation coefficients. CorrGRPO keeps the centered total reward unchanged while balancing the influence of differently scaled rewards on the correlation-based normalization. This allows advantage magnitudes to adapt to reward correlations without the normalization being dominated by large-scale reward components. We compare CorrGRPO with GRPO and other variants on code generation, tool calling, and agent security, using models ranging from 0.5B to 8B parameters. These tasks all involve multiple rewards that can improve together or present tradeoffs. Results show improvements across three domains, including code generation, tool calling, and agent security. Our code is available at https://github.com/HKUST-KnowComp/CorrGRPO.

A single reinforcement-learning run can produce a strong reasoner yet an incomplete teacher: it often amplifies only a subset of the valid solution modes. We argue that reinforcement learning (RL)-trained policies should therefore be viewed as local probes of a multi-basin reasoning solution manifold, rather than as globally reliable supervisors. Based on this view, we propose an expand-then-compress framework that couples teacher construction with multi-teacher policy distillation. In the expansion stage, Residual Group Relative Policy Optimization (RGRPO) trains a sequence of teachers from a common initialization and redirects each later round toward examples not yet covered by the accumulated teacher union. In the compression stage, reliability-gated Teacher-Union On-policy Distillation (TU-OPD) lets the student learn from its own response prefixes. For each example, only reliable teachers contribute, and their sampled-token OPD losses are weighted by their per-example quality. We further introduce Consensus-Residual Decomposition, which preserves a winner teacher's excess token preferences over its reliable peers, preventing specialist behavior from being suppressed during teacher aggregation. Experiments on mathematical reasoning, code generation, and instruction following show that the resulting Qwen3-1.7B student consistently outperforms the strongest individual teacher across all three domains, yielding relative improvements of 2.0%, 8.3%, and 6.9%, respectively, while retaining single-model inference. These results establish a simple but powerful principle: stronger students can be obtained not by selecting a single better teacher, but by deliberately constructing and compressing a complementary teacher union.

Entropy control has become an effective tool in reinforcement learning (RL) of large language models (LLMs), helping balance exploration-exploitation trade-off during alignment process. Such RL paradigm is often conducted on mixtures of heterogeneous tasks, which induce distinct entropy regimes under the same policy, making global or token-level entropy regulation insufficient to corresponding heterogeneous needs of exploration. This heterogeneity further makes GRPO-style normalized advantages induce an entropy-dependent bias, making advantage signals across prompt groups statistically non-comparable. To address this issue, we propose Group Entropy-Controlled Policy Optimization (GEPO), a lightweight extension to GRPO that uses group entropy, estimated from existing grouped samples to perform entropy-conditioned asymmetric advantage shaping. GEPO attenuates positive advantages in low-entropy groups to reduce over-exploitation, and negative advantages in high-entropy groups to preserve exploration, with adaptive thresholds derived from historical entropy statistics. Extensive experiments on two base models across thirteen benchmarks spanning mathematics, physics, science, code generation, and instruction following show that GEPO consistently outperforms GRPO and recent entropy-controlled methods, delivering balanced cross-task improvements while preserving task-specific exploration levels throughout training.

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.

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

Reinforcement learning with verifiable rewards (RLVR) has become an effective paradigm for improving reasoning language models on tasks such as mathematics, coding, and scientific question answering. However, widely used group-relative objectives, such as GRPO, summarize each sampled group with scalar statistics and therefore discard fine-grained relational information among candidate responses. This weakens credit assignment under sparse outcome rewards, especially when multiple generated solutions differ only subtly in reasoning quality. We propose LamPO, a Lambda-Style Policy Optimization method that replaces scalar group advantages with a Pairwise Decomposed Advantage. LamPO aggregates pairwise reward gaps within each response group and modulates each comparison by a confidence-aware weight computed from sequence log-probability differences, while retaining the critic-free and clipped-update structure of PPO-style optimization. When reference solutions are available, we further add a lightweight ROUGE-L-based dense auxiliary reward to reduce reward sparsity. Experiments on AIME24, AIME25, MATH-500, and GPQA-Diamond with Qwen3-1.7B, Qwen3-4B, and Phi-4-mini show that LamPO consistently improves over GRPO and recent RLVR variants, with more stable training dynamics and better sample efficiency.

Training stability remains a critical bottleneck for Group Relative Policy Optimization (GRPO), often manifesting as a trade-off between reasoning plasticity and general capability retention. We identify a root cause as the geometric conflict between plasticity and stability gradients, which leads to destructive interference. Crucially, we argue that deterministic projection methods are suboptimal for GRPO as they overlook the intrinsic stochasticity of group-based gradient estimates. To address this, we propose Probabilistic Conflict Resolution (PCR), a Bayesian framework that models gradients as random variables. PCR dynamically arbitrates conflicts via an uncertainty-aware ``soft projection'' mechanism, optimizing the signal-to-noise ratio. Extensive experiments demonstrate that PCR significantly smooths the training trajectory and achieves superior performance in various reasoning tasks.

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.

Recent progress in multimodal large language models has led to strong performance on reasoning tasks, but these improvements largely rely on high-quality annotated data or teacher-model distillation, both of which are costly and difficult to scale. To address this, we propose an unsupervised self-evolution training framework for multimodal reasoning that achieves stable performance improvements without using human-annotated answers or external reward models. For each input, we sample multiple reasoning trajectories and jointly model their within group structure. We use the Actor's self-consistency signal as a training prior, and introduce a bounded Judge based modulation to continuously reweight trajectories of different quality. We further model the modulated scores as a group level distribution and convert absolute scores into relative advantages within each group, enabling more robust policy updates. Trained with Group Relative Policy Optimization (GRPO) on unlabeled data, our method consistently improves reasoning performance and generalization on five mathematical reasoning benchmarks, offering a scalable path toward self-evolving multimodal models. The code are available at https://github.com/OPPO-Mente-Lab/LLM-Self-Judge.

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.

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

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

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

Test-time reinforcement learning generates multiple candidate answers via repeated rollouts and performs online updates using pseudo-labels constructed by majority voting. To reduce overhead and improve exploration, prior work introduces tree structured rollouts, which share reasoning prefixes and branch at key nodes to improve sampling efficiency. However, this paradigm still faces two challenges: (1) high entropy branching can trigger rollout collapse, where the branching budget concentrates on a few trajectories with consecutive high-entropy segments, rapidly reducing the number of effective branches; (2) early pseudo-labels are noisy and biased, which can induce self-reinforcing overfitting, causing the policy to sharpen prematurely and suppress exploration. To address these issues, we propose Entropy Confidence Hybrid Group Relative Policy Optimization (ECHO). During rollout, ECHO jointly leverages local entropy and group level confidence to adaptively control branch width, and further introduces online confidence-based pruning to terminate persistently low confidence branches, avoiding high entropy traps and mitigating collapse. During policy updates, ECHO employs confidence adaptive clipping and an entropy confidence hybrid advantage shaping approach to enhance training robustness and mitigate early stage bias. Experiments demonstrate that ECHO achieves consistent gains on multiple mathematical and visual reasoning benchmarks, and generalizes more effectively under a limited rollout budget.