Rollout-Level Advantage-Prioritized Experience Replay for GRPO

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-based post-training for reasoning models is increasingly bottlenecked by repeated fresh rollout generation, particularly in agentic settings where environment interaction dominates wall-clock cost. Replay can reduce this burden by reusing past trajectories, but existing methods typically embed it within larger training pipelines involving exploration, experience restructuring, or mixed-policy optimization. This makes replay's own contribution difficult to isolate. We ask a focused question: how far can principled replay selection alone go? We introduce Headroom-Drift Replay, a group-level replay control primitive for GRPO that separates reuse into two decisions. Headroom ranks stored groups by remaining learning value, while Drift gates them by compatibility with the current policy. The fresh on-policy stream remains unchanged, and the method adds no auxiliary generation or training machinery. Across mathematical reasoning, multimodal reasoning, and Agentic Search benchmarks, this single intervention outperforms naive replay and matches or exceeds broader replay methods on Avg Mean@32. In Agentic Search, where environment interaction dominates cost, it delivers comparable quality at materially lower wall-clock time.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a highly effective framework for improving LLM reasoning, with methods such as GRPO among its most successful instantiations. However, GRPO relies on repeated generation of long chain-of-thought rollouts. Training time scales with the number of rollouts, a large fraction of which are uninformative. Thus, GRPO is computationally expensive and unstable. To mitigate this, existing approaches either generate a larger pool of rollouts and filter the most informative prompts, or leverage historical signals for filtering at later stages of training. These strategies offer modest performance gains, but slow down the overall process. To address this, we propose VarIance Guided Online Rollout allocation (VIGOR) which instead of allocating a fixed rollout budget per example, begins with a small number of rollouts for all examples in a batch and iteratively allocates additional rollouts to those with the highest group reward variance until a fixed total rollout budget is reached. Theoretically, we show that under RLVR, reward variance controls the gradient magnitude, and derive VIGOR's closed-form speedup ratio over GRPO, which grows with refinement rounds under Pareto-distributed reward variance. Experiments on mathematical reasoning and coding tasks show that VIGOR reaches target accuracy with up to 2.3$\times$ fewer rollouts on math, reaches GRPO's final coding full pass rate with 1.49$\times$ fewer rollouts, and improves the coding average test pass rate by 3.4 points.