Rethinking Black-Box On-Policy Distillation: A Rubric-based Analysis

On-policy distillation (OPD) is a powerful paradigm for LLM post-training, yet its reliance on teacher logits restricts it to white-box teachers. In this paper, we study whether rubric-based supervision can provide a text-only feedback interface for black-box OPD, and what makes it effective. Our instantiation, Rubric-based On-Policy Distillation (ROPD), induces rubrics by contrasting teacher responses with the student's current rollouts and uses them to score these rollouts for on-policy optimization. We find that, under matched settings, text-only ROPD outperforms logit-based OPD methods on four competition-math benchmarks, reaching the best AIME24 accuracy of standard logit-based OPD with 9.6$\times$ fewer training samples. Our analysis yields three findings: rubric rewards track correctness far better than teacher log-likelihood (AUC 0.90 vs. 0.35); training with them repairs more failed criteria and regresses fewer passed ones than logit-based supervision; and contrasting teacher responses with student rollouts is central to rubric quality. These results position rubric-based OPD as a flexible, black-box-compatible alternative to logit-based OPD. Our implementation is available at https://anonymous.4open.science/r/ROPD-8257.