VESPO: Variational Sequence-level Soft Policy Optimization for Off-Policy LLM Training

Off-policy updates are inevitable in reinforcement learning (RL) for large language models (LLMs) due to rollout staleness from asynchronous training and mismatches between training and inference engines. Naive importance sampling gives an unbiased correction but suffers from high variance, which is amplified by unbounded ratios and autoregressive generation. Prior remedies either rely on scenario-specific engineering, or trade bias for variance via token-level clipping or sequence-level normalization, yet these approaches remain largely heuristic. We propose **V**ariational s**E**quence-level **S**oft **P**olicy **O**ptimization (**VESPO**). By explicitly incorporating variance reduction into a variational formulation, we derive a principled closed-form reshaping kernel that operates directly on sequence-level importance weights, avoids token-level approximation and length normalization, and admits an explicit variance bound for the deployed kernel. Experiments on math reasoning and code generation show that VESPO maintains stable training under severe off-policy conditions (staleness up to $64\times$) and delivers consistent gains across both dense and Mixture-of-Experts (MoE) models, outperforming recent reshaping baselines under matched setup.