Abstract
Group Relative Policy Optimization(GRPO) has become a cornerstone of modern reinforcement learning alignment, prized for its efficacy in foregoing an explicit value-critic by leveraging reward normalization across sampled trajectory cohorts. However, the method's reliance on a monolithic statistical baseline, such as the group mean, collapses the relational topology of the trajectory space into a single scalar, thereby erasing the fine-grained preference information essential for navigating complex, rank-sensitive reward landscapes. To address this issue, we introduce a novel framework, Lambda Policy Optimization (LambdaPO), that addresses this information-theoretic bottleneck by re-conceptualizing advantage estimation from a scalar value to a decomposed, pairwise preference structure. Specifically, the advantage for any given trajectory is formulated as the integrated sum of reward differentials against all peers in its cohort, where each pairwise comparison is dynamically attenuated by the policy's own probabilistic confidence in the established preference. To further mitigate the sparsity of binary outcome supervision, we augment the objective with a semantic density reward, derived from the precision-recall alignment between generated reasoning traces and ground-truth solutions. As a result, our method can mine more fine-grained optimization signals from a group of rollouts, guiding the LLM to a better optima. Experimental results across challenging math reasoning and question-answering tasks demonstrates that LambdaPO improves performance compared to the baseline methods.
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May 20, 2026cs.CL
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 \textbf{LamPO}, a \textbf{Lambda-Style Policy Optimization} method that replaces scalar group advantages with a \emph{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.
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May 6, 2026cs.LG
Reinforcement learning with verifiable rewards (RLVR), particularly Group Relative Policy Optimization (GRPO), has advanced LLM reasoning. However, GRPO suffers from three credit assignment failures: uniform token-level granularity that ignores heterogeneous informational value, uniform polarity that penalizes correct steps and rewards incorrect ones, and zero-variance collapse that erases outcome-driven gradients. We systematically quantify these failures, revealing highly non-uniform token informativeness, widespread step-level polarity misalignment, and substantial training waste. To address these limitations, we propose Entropy-Progress Aligned GRPO (EP-GRPO), a framework that mines the model's intrinsic information flow for dense, self-supervised guidance. EP-GRPO integrates entropy-gated modulation to prioritize high entropy decision pivots, implicit process signals from policy divergence anchored to outcome advantages for directional token-level feedback without external reward models, and cumulative entropy mapping that enables progress-aligned advantage normalization, naturally maintaining gradient flow under zero reward variance. Extensive experiments on mathematical reasoning benchmarks demonstrate that EP-GRPO achieves superior accuracy and efficiency compared to GRPO and its variants. The code will be available.
Song Yu, Li Li, Wenwen Zhao +1
Aug 3, 2026cs.AI
Reinforcement learning has become a central paradigm for improving the reasoning capabilities of large language models. Existing methods generally aim to reduce the failure probabilities induced across problems. In this paper, we introduce a moment-based perspective on policy optimization for LLM reasoning by treating the failure probability of a randomly sampled problem as a random variable and characterizing optimization objectives through its moments. Under this perspective, many existing methods optimize only a single moment of the failure-probability distribution, leaving its broader distributional structure largely uncharacterized. We propose \textbf{M}ulti-\textbf{M}oment \textbf{P}olicy \textbf{O}ptimization (MMPO), a novel policy optimization framework that jointly minimizes multiple moments of the failure-probability distribution. MMPO admits a direct operational interpretation as minimizing the expected truncated time required to obtain the first successful response. Beyond MMPO, we further develop a general moment-transformation framework that systematically induces different moment profiles and provides a unified view of a broader family of policy optimization objectives. Experiments across five mathematical reasoning benchmarks and models of different scales demonstrate that MMPO consistently outperforms strong baselines. We hope this moment-based perspective offers new insights into the design of policy optimization objectives for LLM reasoning.
Yijun Zhang, Yule Xie, Jiaxin Ding +4