Hindsight-Privileged RLVR: Single-Rollout Token Credit Without Group Sampling

arXiv:2610.20497v1 Announce Type: new 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 $1.21\times$, $1.46\times$, and $2.30\times$ 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.

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 $1.21\times$, $1.46\times$, and $2.30\times$ 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.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2610.20497 [cs.LG]

(or arXiv:2610.20497v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.20497 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Hindsight-Privileged RLVR: Single-Rollout Token Credit Without Group Sampling

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