${\text{D}}^3$-MOPD: $\text{D}$ynamic $\text{D}$omain Sche$\text{D}$uling for Efficient Multi-Teacher Distillation

Multi-teacher on-policy distillation (MOPD) distills several domain-expert teachers into a single student by minimizing per-domain reverse-KL divergence on the student's own rollouts. Existing approaches typically fix the per-domain data mixture before training, overlooking the fact that different domains converge at substantially different rates: some plateau early while others continue to improve throughout the training budget. A fixed mixture therefore wastes compute on fast-converging domains and undertrains slower-converging ones. To address this, we propose D${}^3$-MOPD ($\text{D}$ynamic $\text{D}$omain Sche$\text{D}$uling for MOPD), a zero-overhead scheduler that repurposes the per-domain reverse-KL signal already produced during training to adapt the domain mixture online. Running asynchronously outside the training process, an off-process watcher periodically tracks each domain's KL trajectory, estimates remaining headroom and current improvement rate, and accordingly adjusts the domain sampling ratios without altering the core training loop. Our D${}^3$-MOPD scales naturally to arbitrary numbers of domains, and the expected benefit grows as more domains introduce more diverse convergence patterns for the scheduler to exploit. On a Qwen3.6-35B-A3B student distilled from four domain-expert teachers, D${}^3$-MOPD closes 97% of the average student-to-teacher performance gap, compared with 63% for vanilla MOPD, reaches the same peak performance with an approximately $3\times$ reduction in rollout steps, and surpasses the specialist teachers on three of seven benchmarks.