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arXiv · 2609.25048

Teaching a Moving Student: Rethinking the Curriculum of On-Policy Distillation

Lingxiang Hu·Tianle Xia·Yiding Sun·Ming Xu·Linfang Shang·Lan Xu·Ning Zheng·Wei Xu·Jie Jiang
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Abstract

In on-policy distillation (OPD), the student determines which states receive teacher supervision. As its policy evolves, earlier response prefixes become less likely even though teacher-student disagreement on them persists. Under matched trajectory and optimization budgets, neither more queries nor more frequent rollout resampling is uniformly beneficial. Current-policy rollouts outperform initial-policy rollouts at shorter response budgets, but this ranking reverses at longer budgets. Replaying initial-policy rollouts after current-policy training improves accuracy, whereas replaying fixed recent rollouts does not reproduce the gain. We propose R-OPD, a gradient-triggered curriculum that adaptively selects when to revisit initial-student trajectories. When changes in mean gradients fall within minibatch-level variation for two consecutive comparisons, training switches from the next iteration onward to initial-policy replay. Across eight mathematics benchmarks and three training-data orders, R-OPD improves average accuracy over continued current-policy sampling by 2.25/4.44 percentage points at 16K/32K for a 0.6B student and 2.81/6.15 points for a 1.7B student. With a 30B-A3B teacher, it improves 8B accuracy by 4.05 points at 32K. At 32K, R-OPD exceeds a fixed schedule of 40 current-policy updates followed by 20 replay updates by 1.39/1.66/1.85 points for 0.6B/1.7B/8B. At the same generation cap, R-OPD also produces longer responses, suggesting that well-timed revisits help students use more of their reasoning capacity.

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Lingxiang Hu, Tianle Xia, Yiding Sun, Ming Xu, Linfang Shang, Lan Xu, Ning Zheng, Wei Xu, Jie Jiang. 2026-09-26. Teaching a Moving Student: Rethinking the Curriculum of On-Policy Distillation. https://arxiv.org/abs/2609.25048

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