GAC: Stabilizing Asynchronous RL Training for LLMs via Gradient Alignment Control

Asynchronous reinforcement learning (RL) improves the efficiency of large language model post-training but introduces stale rollouts generated by earlier policies. Theoretical understanding of how this staleness affects convergence and how to mitigate its impact remains limited. We derive a convergence bound for GRPO-style algorithms that explicitly characterizes the tradeoff between the gradient estimator's second moment and bias. For trajectory-level importance-weighted estimators, our analysis shows that once the second moment is uniformly controlled, delay enters the bound through the bias introduced by clipping or rescaling. Guided by this insight, we propose a novel group mass capping GRPO (GMC-GRPO) method, which minimizes a ratio-based bias bound within a class of weighted estimators sharing a common second-moment guarantee. We establish convergence guarantees for asynchronous GMC-GRPO and show that, compared with TIC-GRPO, it improves the threshold dependence of the fourth-order delay term from $O(ε^{-4})$ to $O(ε^{-2})$ as $ε\to0$, where $1+ε$ is the ratio threshold. Under local policy overlap, the delay-dependent term decreases as $G^{-2/5}$ after tuning the step size, where $G$ is the group size. For fixed behavior and current policies, the bias introduced by group rescaling also vanishes as $G\to\infty$, whereas the bias from trajectory-wise clipping can persist. Experiments across Qwen3 models and reasoning benchmarks demonstrate improved robustness to stale rollouts, with GMC-GRPO achieving the best performance among stable baselines under large rollout delays.

Asynchronous reinforcement learning has become increasingly central to scaling LLM post-training, delivering major throughput gains by decoupling rollout generation from policy updates. However, widely used policy-gradient objectives such as REINFORCE and GRPO suffer under high asynchrony: stale rollouts produce heavy-tailed importance weights, so a small number of trajectories dominate updates and the policy-gradient estimator becomes markedly higher variance. Through systematic analysis on math, reasoning, and tool-use benchmarks, we find that this increasing variance is reliably predicted by collapsing effective sample size (ESS), which prior stabilization methods largely fail to address. Motivated by this diagnosis, we introduce $\textbf{V}$ariance $\textbf{C}$ontrolled $\textbf{P}$olicy $\textbf{O}$ptimization ($\textbf{VCPO}$), a method that (i) dynamically scales the learning rate with ESS to dampen unreliable updates and (ii) applies a closed-form minimum-variance baseline for off-policy settings, without a critic model and adding minimal overhead. Empirically, across math and general reasoning benchmarks, this enables robustly stable asynchronous training compared to previous stabilization and algorithmic methods, even in highly off-policy regimes (128 steps off-policy). In a long-horizon, tool-use task, VCPO matches synchronous performance while delivering a 2.5$\times$ speedup in training time. Code is available at: https://github.com/mit-han-lab/vcpo

Fully asynchronous reinforcement learning (RL) improves resource utilization in large language model post-training by overlapping rollout generation with policy optimization, but it also introduces policy lag as trajectories are generated and queued while the trainer continues to update. We study how this lag accumulates over a trajectory's lifetime and how it can be controlled without sacrificing the wall-clock benefits of asynchronous execution. We decompose trajectory staleness into Generation Staleness, accumulated before rollout completion, and Waiting Staleness, accumulated after a completed trajectory enters the pool. Motivated by this decomposition, we introduce PACE (Pool-Aware Control of Effective Staleness). PACE converts excess pool occupancy into an adaptive rejection budget and ranks completed trajectories using an effective-staleness score that combines Waiting Staleness with prefix-aware Generation Staleness. This avoids penalizing long or interrupted rollouts solely because they span multiple policy versions. In single-turn mathematical reasoning, PACE improves the six-benchmark average validation accuracy by 18.7% over unfiltered asynchronous RL at the same wall-clock budget and matches synchronous RL performance with 47.1% less GPU time. PACE also improves validation performance in multi-turn tool-integrated reasoning, outperforming both synchronous and unfiltered asynchronous RL. Further experiments with the mixture-of-experts model and an alternative RL algorithm support its applicability across model architectures and training algorithms.