What are Key Factors for Updates in RL for LLM Reasoning?

RL with verifiable rewards can substantially improve LLM reasoning, yet standard GRPO-style training often treats easy, hard, and learnable questions alike through uniform sampling and weighting, leading to inefficient compute allocation. We study GRPO by tracking token log-probabilities, group-normalized advantages, and the induced token-level update weights. This reveals three recurring dynamics as training proceeds: (1) confidence inflation, (2) advantage contraction, and (3) hierarchical convergence. These findings suggest that the utility of each update depends strongly on both question difficulty and the model's current competence. Motivated by this, we propose Confidence and Difficulty-adaptive Policy Optimization (CoDaPO), which assigns each question a bounded value from rollout confidence and empirical difficulty. CoDaPO then uses this value to reweight policy updates and resample high-value learnable questions within mini-batches, thereby increasing discovery within the learnable band under a fixed compute budget. Across twelve benchmarks, CoDaPO consistently improves accuracy over existing RL methods. Our code is publicly available at https://github.com/tmlr-group/CoDaPO.

Reinforcement Learning with Verifiable Rewards (RLVR) is a powerful paradigm for improving the reasoning capabilities of large language models (LLMs). However, existing RLVR methods typically rely on on-policy optimization from scratch, resulting in high sampling costs and inefficient utilization of accumulated experience. As model capabilities and policy behaviors evolve during training, recent attempts to reuse experience via fixed reasoning trajectories further suffer from policy mismatch. Motivated by these limitations, we argue that experience in RLVR should not be reused as fixed reasoning trajectories, but instead expressed in a policy-adaptive manner. In this work, we propose Experience-Augmented Policy Optimization (EAPO), which leverages a prior RL-optimized policy as an action-level experience prior and selectively injects experience at critical decision points during rollout. To ensure stable and unbiased learning from experience-augmented rollouts, EAPO further incorporates an adapted importance sampling scheme. Experiments on using Qwen-2.5-math 7b and Qwen-3-8B on five different benchmarks demonstrate that EAPO consistently improves reasoning performance over state-of-the-art RLVR methods.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a powerful paradigm for enhancing the reasoning capabilities of large language models (LLMs). However, its effectiveness is substantially hindered by the prevalence of ineffective training data: many sampled prompts yield response groups that are either entirely correct or entirely incorrect, resulting in zero-variance rewards and limited learning signals. Recent state-of-the-art methods address this issue through extensive LLM rollouts to filter ineffective samples, but at the cost of considerable computational overhead. Alternative approaches, including predictive sampling and trajectory replay, aim to improve data efficiency but often remain insufficient and may introduce additional issues such as systematic bias or suboptimal constraints. To address these limitations, we propose Group Prioritized Off-Policy Optimization (POPO), a simple yet effective framework that fully exploits effective training batches without additional rollout overhead. POPO comprises two key components: prioritized group replay and decoupled off-policy optimization. The former replaces ineffective on-policy groups with effective off-policy groups via a recency-based replay mechanism that jointly considers sample quality and the degree of off-policiness. To further mitigate the off-policy gap, POPO employs decoupled importance sampling to correct off-policy bias while maintaining stable policy updates under consistent trust-region constraints. Empirical evaluations across diverse reasoning tasks, including mathematics, planning, and visual geometry, demonstrate that POPO substantially accelerates RL finetuning and achieves strong reasoning performance with significantly fewer rollouts.