Outcome-Guided On-Policy Self-Distillation
On-policy self-distillation (OPSD) provides denser token-level supervision and better computational efficiency than Reinforcement Learning with Verifiable Rewards (RLVR). However, this denser supervision may introduce substantial noise and training instability. Existing improvements often rely on high-variance per-token statistics and introduce extra hyperparameters and trade-offs. Based on the advantage formulation in RLVR, we analyze the OPSD objective from the same perspective, incorporating outcome correctness signals. We find that vanilla OPSD imposes insufficient penalties and excessive rewards on incorrect trajectories because it applies a fixed divergence objective regardless of outcome correctness. Furthermore, the reliability of teacher supervision is associated with both trajectory outcome and the cumulative average teacher entropy along the rollout. Based on these observations, we propose Outcome-Guided On-Policy Self-Distillation (OG-OPSD), which dynamically adapts both the divergence objective and distillation position according to binary outcome rewards and the cumulative average teacher entropy. Extensive experiments show that OG-OPSD consistently improves the performance of vanilla OPSD and multiple strong baselines in mathematical reasoning, multimodal reasoning, and out-of-distribution tasks across Qwen3 models at 1.7B, 4B, and 8B scales, as well as Qwen3-VL-2B.