Adaptive-Policy Distillation: Knowledge Injection under Information Asymmetry

On-policy distillation (OPD) trains a student model on its self-generated trajectories with dense token-level teacher feedback. However, naive OPD may suffer from teacher unanchoring, where the student's reasoning trajectory drifts far from the teacher, causing the teacher to be queried on states it would hardly visit and thus provide unreliable supervision. We propose Interactive-Policy Distillation (IPD), which applies adaptive teacher intervention to the student rollout. Under a bidirectional propose-and-verify state machine, the student and teacher alternately exchange their roles as proposer and verifier, and collaboratively generate mixed-source trajectories. Then different supervisions are applied according to the source of each token. This bidirectional propose-and-verify mechanism and the source-split loss make IPD not only a more performant distillation method, but also a unified bridge between on-policy and off-policy paradigms. To make the interleaved dual-model rollouts more efficient, we also design a dedicated fused inference engine that co-hosts both models in one serving instance with separate KV caches and instantiates the state machine model to distribute, collect, and process requests. On math reasoning tasks and across multiple teacher-student model pairs, student models trained with IPD not only outperform those trained with OPD, but also demonstrate higher data efficiency. Specifically, when distilling Qwen3-30B-A3B into Qwen3-1.7B-Base, IPD brings a +3.28 mean@8 and a +3.28 best@8 benchmark-averaged accuracy improvement compared with OPD. Besides, IPD only consumes about 1/4 of the training examples and steps to outperform OPD trained on the whole training dataset for one epoch. We also investigate the impact of different loss variants and takeover / handback configurations, and demonstrate the robustness of IPD on different training data.

On-policy distillation (OPD) offers dense token-level supervision as an alternative to the sparse outcome-level advantages of reinforcement learning with verifiable rewards (RLVR). However, the teacher scores student-generated trajectories that are inherently off-policy for it, so the reliability of its supervision, and hence the source of the student's improvement, remains unclear. We quantitatively analyze teacher supervision during OPD training and find substantial noise whose prevalence increases with teacher scale. Surprisingly, the student policy is insensitive to such noise, converging to comparable performance regardless of whether noisy supervision is retained or removed. Does OPD distill at all? By analyzing what drives its gains, we find that learning concentrates on low log-probability tokens, and using a single fixed negative advantage matches the performance of teacher-provided ones. This suggests that OPD works largely by suppressing low log-probability tokens, which requires no teacher. These findings motivate On-Policy Self-Adaptation (OPSA), a supervision-free method using entropy-adaptive negative advantages. It assigns stronger learning signals to high-entropy positions, suppressing tail tokens, and evenly redistributing probability mass among head tokens. Compared with the base Qwen3-1.7B, OPSA improves Avg@32 by 35.41 points on AIME24, corresponding to a 263% relative gain, and more than doubles Pass@32 across all three benchmarks. It also outperforms OPD by 16.77 points in Avg@32 on AIME24. Extensive experiments and analyses across model families and tasks further demonstrate its effectiveness and generalizability.

On-policy distillation (OPD) is increasingly studied as a cheaper alternative to reinforcement learning, yet it remains a form of knowledge distillation (KD) that relies on teacher supervision. We revisit OPD from the KD perspective by asking where the teacher's advantage lies along student-generated trajectories. Controlled token flips at teacher-student disagreements directly measure the accuracy gained from teacher corrections. Single-token flips yield a modest average gain on selected failed trajectories, whereas repeated flips raise accuracy from 28.4% to 74.5%, close to the teacher's 76.9%. Gains continue to accumulate with more flips, but mass- and KL-based selection outperform random flips by 15-18 percentage points at counts of similar magnitude. Selective intervention remains useful after OPD, but greater argmax agreement does not consistently improve accuracy across model pairs. We advocate training schedules that learn more valuable teacher corrections while maintaining distributional stability. Controlled flips and fork-resolution analysis evaluate OPD beyond accuracy by measuring which teacher preferences the student acquires and what further correction can recover.