LamPO: A Lambda Style Policy Optimization for Reasoning Language Models

• URL: http://arxiv.org/abs/2605.21235v1
• Date: Wed, 20 May 2026 14:24:11 GMT
• Title: LamPO: A Lambda Style Policy Optimization for Reasoning Language Models
• Abstract summary: 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.<n>We propose textbfLamPO, a textbfLambda-Style Policy Optimization method that replaces scalar group advantages with a emphPairwise De Advantage.<n>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
• Score: 34.349722314481824
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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