Title: What are Key Factors for Updates in RL for LLM Reasoning?
Primary area: foundation or frontier models, including LLMs
Keywords: reinforcement learning, large language model, reasoning

Abstract: Reinforcement Learning from Verifiable Rewards (RLVR) has emerged as a promising framework for enhancing the reasoning ability of large language models. However, much of the existing work is guided by heuristic intuition, leading to divergent algorithmic choices, even contradictory ones that nevertheless report empirical gains. To better understand this phenomenon, we conduct a theoretical analysis of RLVR updates. Our study reveals that differences in off-policy degree, determined by the number of gradient steps per rollout, substantially affect the distribution of importance sampling ratios and their clipping behavior, thereby altering which tokens dominate the update. Building on this insight, we characterize gradient expectation as the central quantity governing update dynamics and analyze the roles of token probability, advantage, and importance sampling ratio. Motivated by these findings, we propose Adaptive Clip Policy Optimization (ACPO), which adjusts clipping boundaries across token groups according to the empirical variance of their importance sampling ratios. Experiments on models of varying scales (3B, and 7B) and diverse reasoning benchmarks—including mathematical problem solving, tabular question answering, and logic puzzles—show that ACPO outperforms strong baselines such as DAPO and CISPO. These results demonstrate that principled, analysis-driven approaches yield more robust and effective RLVR methods.