Composing What Each Teacher Learned: Multi-Teacher On-Policy Distillation through Teacher-Relative Shifts

Hejian Sang, Zhengze Zhou, Shayan Mohajer Hamidi, Xiaomin Li, Rohit Jain +1

Multi-teacher on-policy distillation (MOPD) is used in two settings. In common-domain composition, several teachers score each student rollout from one prompt domain and their signals form a single target; in routed-domain distillation, prompts from different domains are assigned to the corresponding specialist. Both settings usually transfer each teacher's endpoint policy, which mixes what post-training changed with preferences inherited from the teacher's base. We introduce $Δ$-MOPD, which transfers each teacher's teacher-minus-base logit shift re-anchored at the student's frozen initialization, and compare it with endpoint supervision in both settings while holding teacher selection fixed. We first expose the mechanism that impedes endpoint transfer: inherited base pull can exceed the post-training shift. Removing it reduces the teacher-term norm ratio and target--student KL. Across our experiments, the results suggest that shift targets are particularly useful when teacher signals are combined at a state. With three composed teachers, $Δ$-MOPD exceeds endpoint composition by $4.11$ Math and $1.95$ five-benchmark points; with two, it matches endpoint accuracy. Under phased…