[Submitted on 14 Oct 2026 (v1), last revised 15 Oct 2026 (this version, v2)]
Authors:Wei Chen, Yubing Wu, Zhou Xu, Haoyue Zhang, Delu Zeng, Jiahao Wang, Junmei Yang, Pan tiewen, Jingfeng Liu, Zhiheng Zhou, Bo Li, Min Chen
Abstract:Reinforcement learning with verifiable rewards (RLVR) trains language models from checked task outcomes, but assigning a terminal reward to individual reasoning tokens or actions remains difficult. Group-relative methods such as Group Relative Policy Optimization (GRPO) sample several attempts per prompt, but lose their reward-based learning signal when all attempts receive the same outcome. We propose Hindsight-Privileged RLVR (HP-RLVR), a single-rollout method that turns a completed trajectory’s own future into token-level update weights. The generating policy snapshot scores each eligible token under its causal history and under a hindsight context containing the realized future and verifier feedback. A normalized Jensen–Shannon divergence between the two views weights the reward relative to a historical baseline, yielding bounded token credit for both successful and failed attempts, with no reference solution or learned critic. In paired Qwen3-8B runs over a shared $100$-step schedule, HP-RLVR trains $1.21times$, $1.46times$, and $2.30times$ faster than GRPO on mathematics, code generation, and ALFWorld, using one eighth the rollouts per prompt. Accuracy is comparable overall, with HP-RLVR ahead on mathematics at all three sizes and GRPO ahead on code and ALFWorld. In ALFWorld, $43.2%$ (4B) and $49.0%$ (8B) of GRPO’s gradient-norm records are zero, versus none for HP-RLVR.
Submission history
From: Wei Chen [view email]
[v1] Wed, 14 Oct 2026 17:06:59 UTC (176 KB)
[v2] Thu, 15 Oct 2026 06:36:16 UTC (176 KB)
