Are Dense Rewards Worth Their Tokens in GRPO?

Vikash Singh, Weicong Chen, Debargha Ganguly, Yanyan Zhang, Mohsen Hariri +14

RLVR trains language models to reason by rewarding correct final answers. A widely used algorithm, group-relative policy optimization (GRPO), gives every token of a solution the same credit, so dense process rewards have been proposed to credit intermediate steps, for example with a Monte-Carlo reward that scores each step by sampling continuations from it. Comparing such a reward with GRPO per training update, or vetting it with a gradient test on a single batch, leaves out what it costs: in our setting, the continuations alone take 91% of all generated tokens. We introduce a matched-compute protocol that gives every training intervention the same budget, measured in generated tokens and training GPU-hours, and tests it in preregistered studies with controls for side effects. Across 1,668 runs on six models, matching compute reverses the ranking. On Qwen2.5-1.5B, the Monte-Carlo reward leads standard GRPO per update, yet ends 14.3 percentage points lower at equal tokens and 7.8 points lower at equal training time, and none of four dense-reward variants outperforms GRPO even with as much training time. A per-token gradient test orders these rewards as training does but…