Reinforcement learning is crucial for improving large language models' reasoning and generalization. It relies on massive rollouts whose lengths become increasingly long-tailed as context windows grow. In on-policy training, these long-tail rollouts can result in GPU bubbles, reducing system utilization and limiting RL scalability. Asynchronous or partial-rollout methods improve throughput by relaxing synchronization, but inevitably introduce stale off-policy samples (trajectories) that may hurt final accuracy. Existing approaches mainly mitigate this off-policy issue by reweighting off-policy samples during training, yet they can still leave a performance gap compared to fully on-policy training. In this work, rather than passively reweighting samples during training, we propose RollVerify, a lightweight RL framework built on partial rollout that actively verifies and repairs samples before they enter training. Specifically, it introduces an off-policy shift metric OPS, to quantify the off-policy deviation of partially generated trajectories. Guided by the OPS constraint, RollVerify performs both sequence-level and token-level verification to identify and truncate invalid suffixes of trajectories. This yields high-quality samples that protect the models' accuracy while preserving the efficiency gains of partial rollout. Experiments on mathematical and tool-assisted mathematical reasoning show that RollVerify achieves accuracy comparable to on-policy training while reducing training cost. Additional code-generation results provide preliminary evidence beyond mathematics.

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