BAS-OPD: Budget-Aware Selective On-Policy Self-Distillation for Fine-Grained Multimodal Perception

Multimodal large language models (MLLMs) often struggle with fine-grained visual perception when critical evidence appears in local regions. On-policy distillation (OPD) can transfer privileged regional knowledge into a single-pass full-image policy, but formulations typically supervise every eligible rollout. This implicitly treats teacher feedback as equally valuable, even though the student policy evolves during on-policy training and the supervision value of different rollouts need not remain uniform. We therefore formulate privileged OPD as an online rollout-selection problem to study which rollouts merit supervision and introduce Budget-Aware Selective On-Policy Self-Distillation (BAS-OPD). The student generates a full candidate pool, while BAS-OPD selectively assigns crop-teacher supervision using random, uncertainty-based, or learned utility-based selection. Because the target utility is observable only after teacher scoring, we adopt a lightweight predictor to estimate it beforehand from detached student-side rollout statistics. Only selected rollouts enter the crop-teacher forward pass during training, while inference remains single-pass and selector-free. Across seven benchmarks, learned selection outperforms random and entropy-based selection at the same ratio, showing that how teacher supervision is allocated matters in addition to how much is used. With Qwen3.5-4B/9B, our method achieves 81.60%/84.23% average accuracy, exceeding full querying by 1.84/2.04 percentage while using only 25% of eligible rollouts and scoring 15.78%/16.02% of teacher-scored tokens. Thus, supervising more rollouts does not necessarily improve downstream performance.