On-policy distillation has the same systems bottleneck as RL: rollouts dominate training time on reasoning workloads. Going async fixes throughput but feeds the learner stale-policy data, and what staleness does to OPD specifically was unstudied.
The clean finding is that KL direction decides robustness. Teacher-weighted forward KL shrugs off stale rollouts, student-weighted reverse KL breaks under them, and for the reverse-KL case nothing from async RL beats just recomputing the signal under the current student.
Finite teacher-score caches then turn the estimator into a bias-variance tradeoff, which is the case for multi-sample Monte Carlo.
AsyncOPD: How Stale Can On-Policy Distillation Be?
Paper: