Two Clocks: Why Larger Rollout Batches Learn Slower but Fail on Schedule in Reinforcement Learning with Verifiable Rewards

Reinforcement learning with verifiable rewards (RLVR) relies on costly model-generated responses, motivating larger rollout batches and square-root learning-rate scaling. Reported to approximately preserve progress per sample with one optimizer step per rollout, this rule is less understood in practical multi-step training. We develop a two-clock framework that separates the samples needed to make progress from those consumed before collapse. Under a local quadratic model, the square-root rule preserves first-order drift per sample but not progress: larger batches take fewer, longer updates and lose more to curvature, yielding a learning-rate-dependent critical batch beyond which sample e...

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