O$^2$PD: Overlap-Gated On-Policy Distillation on Reliable Prefix

Shuaishuai Zu, Jihao Zhao, Pengfei Li, Guanghuan Fang, Ben Feng +3

On-policy distillation (OPD) supplies dense token-level supervision by aligning a student to the teacher's next-token distribution on its own generated rollouts. Existing works mostly implement top-$k$ OPD, applying reverse Kullback-Leibler ($\RKL$) divergence between the teacher's and the student's renormalized distributions over teacher top-$k$ support. However, the teacher scores student-generated rollouts that are inherently off-policy for itself, leaving the reliability of its next-token guidance unclear. Restricting the divergence to the teacher top-$k$ support also discards the remaining mass outside that support. These gaps leave two questions implicit: 1) which tokens to align, and 2) how to align those tokens. To answer these questions, we propose Overlap-gated On-Policy Distillation (O$^{2}$PD). As for 1), we quantitatively analyze the reliability of teacher supervision and find that alignment on the student's trajectory prefix is more reliable than alignment on the full context. Therefore, our O$^{2}$PD is applied only to the 20\% prefix tokens of each student rollout. As for 2), we theoretically characterize two problems of top-$k$ OPD: the \emph{Teacher-support…