Reinforcement learning for large language model post-training often reuses each batch of sampled rollouts for several gradient passes to amortize the cost of generation. Under such multi-pass reuse, existing objectives fail in different ways: unclipped updates collapse as the policy drifts away from the sampling policy, adding a negative baseline avoids collapse but reinforces every sampled response, and PPO-style ratio clipping cuts off gradients abruptly. We first ask why reuse is fragile. Measuring how well an update estimated from a small rollout group aligns with the KL-regularized target on held-out rollouts of the same prompts, we find that this alignment drops by nearly an order of magnitude from in-sample to held-out rollouts across three base models, suggesting that repeated passes largely overfit the sampled group. Motivated by this finding, we propose Bounded Residual-Aligned Training (BRAT), motivated by a proximal update toward a bounded reweighting of the sampling policy. BRAT assigns each token a gradient weight that decreases linearly with its probability ratio and vanishes at a trust-region boundary, and normalizes group-centered rewards by their maximum magnitude, keeping advantages zero-mean and bounded without extra hyperparameters. With four reuse passes, BRAT avoids training collapse, limits policy drift, and achieves higher average accuracy with lower seed variance on most benchmarks.

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