Prosperity before Collapse: How Far Can Off-Policy RL Reach with Stale Data on LLMs?

Reinforcement learning has been central to recent advances in large language model reasoning, but most algorithms rely on on-policy training that demands fresh rollouts at every update, limiting efficiency and scalability. Asynchronous RL systems alleviate this by decoupling rollout generation from training, yet their effectiveness hinges on tolerating large staleness in rollout data, a setting where existing methods either degrade in performance or collapse. We revisit this challenge and uncover a \emph{prosperity-before-collapse} phenomenon: stale data can be as informative as on-policy data if exploited properly. Building on this insight, we introduce \textbf{M2PO} (Second-Moment Trust Policy Optimization), which constrains the second moment of importance weights to suppress only extreme outliers while preserving informative updates. Notably, M2PO sharply reduces the fraction of clipped tokens under high staleness (from 1.22\% to 0.06\% over training), precisely masking high-variance tokens while maintaining stable optimization. Extensive evaluation across six model scales (from 1.7B to 32B) and eight math reasoning benchmarks and one coding benchmarks shows that M2PO delivers stable off-policy training even with data stale by \underline{\emph{at least 256 model updates}} and matches on-policy performance. Our code is available at https://github.com/Infini-AI-Lab/M2PO/.