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

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×, 1.46×, and 2.30× 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.