AGPO: Adaptive Group Policy Optimization with Dual Statistical Feedback

Group relative policy optimization for reinforcement learning with verifiable rewards (RLVR) typically uses a fixed importance-sampling (IS) ratio clipping boundary across all rollouts. We identify a key limitation: rare correct rollouts on harder problems and abundant correct rollouts on easier problems are clipped at comparable rates, despite contributing very different learning signals. Rollouts with low group success exhibit larger IS ratios and carry stronger gradient signal for exploration and solving new problems, yet are disproportionately suppressed by fixed clipping. To address this, we propose Group Adaptive Clipping Policy Optimization (GAPO), a plug-in modification to GRPO methods that adapts the clipping boundary to the rollout advantage. GAPO is motivated by a reverse-KL trust-region perspective, which suggests that rollouts with larger learning signal should receive proportionally greater update headroom. GAPO requires no reward shaping and preserves the standard PPO/GSPO surrogate while adapting only the clipping threshold. Across Qwen and Llama models, GAPO consistently improves both Pass@1 and Pass@k over fixed clipping and advantage-shaping baselines on math reasoning and coding benchmarks where the pass rates by the base model are relatively low.

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.

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.