Quantifying Empirical Compute-Supervision Tradeoffs in RLVR

Reinforcement learning with verifiable rewards (RLVR) has become a standard paradigm for post-training language models, but in practice, verifiers are rarely perfect. Recent theoretical work predicts that verifier noise affects the rate of learning but not its final outcome, implying that sufficient compute should close any gap induced by imperfect supervision. We test this prediction empirically by post-training Qwen2.5 (0.5B, 1.5B) with GRPO on GSM8K while injecting controlled false-positive and false-negative noise into the binary correctness signal, and varying rollouts per prompt as a compute axis. In practice, the gap in validation accuracy persists under substantial compute scaling, with returns to compute that are sharply diminishing. We further find a structural asymmetry where false negatives monotonically degrade performance more quickly than false positives. These findings suggest verifier quality and training compute are not interchangeable, and that reducing false negatives is a more effective lever than scaling compute alone.