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arXiv · 2609.16937

Beyond Token-Local Imitation: Reward-Compatible Temporal Credit Assignment for On-Policy Distillation

Shiqi Liu·Zeyu He·Letian Tao·Guojian Zhan·Jiaxin Gao·Feihong Zhang·Jingliang Duan·Wei Xiong·Kehua Sheng·Bo Zhang·Yang Guan·Shengbo Eben Li
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Abstract

On-policy distillation (OPD) has emerged as an effective approach for large language model post-training, yet existing objectives face a trade-off between objective fidelity and optimization stability. Token-level OPD provides stable but local supervision, whereas sequence-level OPD captures future credit at the cost of horizon-dependent variance. We establish a unified temporal-credit view of these formulations, showing that practical token-level OPD can be interpreted as a temporal approximation to the sequence-level reverse-KL gradient. Building on this connection, we propose $γ$OPD (GammaOPD), which uses discounted temporal credit assignment to balance long-horizon supervision and optimization stability, while admitting a horizon-independent variance bound. We further develop a reward-compatible bounded mixing (RBM) mechanism for $γ$OPD that balances verifiable outcome feedback with the discounted OPD advantage to move beyond purely teacher-dependent optimization. Experiments on mathematical and code reasoning demonstrate consistent improvements over existing OPD methods across vanilla, size-mismatched, and multi-teacher distillation settings.

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Shiqi Liu, Zeyu He, Letian Tao, Guojian Zhan, Jiaxin Gao, Feihong Zhang, Jingliang Duan, Wei Xiong, Kehua Sheng, Bo Zhang, Yang Guan, Shengbo Eben Li. 2026-09-19. Beyond Token-Local Imitation: Reward-Compatible Temporal Credit Assignment for On-Policy Distillation. https://arxiv.org/abs/2609.16937

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