Persistent Negatives for Adversarial Black-Box On-Policy Distillation

Haixu Ma, Saad Lahrichi, Weiwei Li, Kevin Han, Weiqiang Wu +9

Black-box On-Policy Distillation (OPD) seeks to improve a student from its own generations when the teacher provides sampled responses but not token probabilities. Adversarial distillation offers one route: it learns a discriminator over prompt-matched teacher and student responses and uses its score as the policy reward. However, sampling discriminator negatives from the latest student at each step couples the learned reward to a negative distribution that changes after every policy update. We address this moving-target problem with persistent-negative adversarial distillation, a live-pool method that replaces a fraction of each discriminator batch with historical, prompt-matched teacher--student comparisons. Under matched discriminator compute, historical comparisons train the discriminator, while GRPO remains on-policy with fresh student responses. Our analysis identifies the Bayes-optimal reward as a teacher-to-negative log-density ratio and, under explicit assumptions, shows how persistent negatives anchor the discriminator and reduce reward-estimation MSE relative to fresh-negative training. Across two student families, three judges, and four judged-chat benchmarks,…