Future Policy Approximation for Offline Reinforcement Learning in LLM Reasoning

Reinforcement learning (RL) has emerged as a key driver of post-training for complex reasoning in large language models (LLMs), yet online RL introduces substantial instability and computational overhead. Offline RL offers a compelling alternative by decoupling generation from training; however, offline algorithms for reasoning remain under-optimized relative to their online counterparts. We revisit the potential of policy-gradient-style offline RL and address a central challenge in offline learning: gradient entanglement. In long-horizon reasoning trajectories, correct and incorrect solutions share substantial token overlap, causing gradient updates from incorrect trajectories to suppress tokens that are also critical for correct ones. We propose Future Policy Approximation (FPA), a simple offline policy-gradient method that weights gradients using an estimate of the future policy rather than the current policy, enabling proactive gradient reweighting. We estimate the future policy through logit- space extrapolation. Across three models, seven mathematical reasoning benchmarks, and three code-generation benchmarks, FPA consistently improves over strong offline baselines, including DPO, RPO, KTO, and vanilla offline RL. FPA stabilizes long-horizon training, where vanilla objectives degrade, and achieves accuracy comparable to state-of-the-art RLVR methods such as GRPO and DAPO at a fraction of the GPU hours.