On-policy distillation (OPD) trains a student on its own generated responses using dense, token-level supervision from a stronger teacher. Vanilla OPD treats all teacher signals equally, assuming that the teacher's supervision is equally important for every token. However, teacher signals at different tokens may have very different effects on the student's performance: some correct important reasoning errors, while others have little effect on the final answer. Motivated by this observation, we introduce Dr. OPD (OPD Done Right), which defines the optimal weighted OPD to maximize the student's performance. We formulate Dr. OPD as a bilevel optimization problem in which the student learns from weighted teacher supervision, while the weights are selected to maximize the expected reward of the resulting student. To solve Dr. OPD, we develop an efficient iterative solver that updates the token weights and student policy alternatively. At each round, it updates weights in closed form and then takes one gradient step on the resulting weighted OPD objective. Under regularity conditions, we show that this weighted update achieves a higher expected reward than a vanilla OPD update. Empirically, across strong-to-weak and same-size distillation on math and code, Dr. OPD consistently outperforms all evaluated baselines. In particular, in the strong-to-weak distillation setting, Dr. OPD improves average math performance by 9.7 points over vanilla OPD, and enables the smaller student to surpass its larger teacher.
Figures & tables
Figure 1: Illustration of Dr. OPD. Left: vanilla OPD assigns the same weight to every teacher signal, while Dr. OPD adapts the weights according to their benefit to the student. Right: student rollouts receive teacher and outcome-reward signals, whose gradient alignment determines token credits. These credits are converted into weights for distillation, where λ controls the weighting strength.
Figure 2: Empirical gains. Across both distillation setups, Dr. OPD consistently outperforms existing baselines and even produces a student that surpasses its teacher (Full results in Section 5.2 ).
Appendix figures & tables2 assets
Supplementary material from the paper’s appendix.
Appendix
Hyperparameter
Value
Learning rate
1×10−5
LR schedule
constant
Gradient clipping
1.0
Batch / Mini-batch size
128
Rollouts per prompt K
8
Rollouts per step
1024
Appendix
Table 4: Hyperparameters shared by all methods and both tasks.
Method
Hyperparameters
OPD
None
ExOPD
λ=1.25 ; the initial student as reference policy
OPD+GRPO
Equal weighting (1:1) of the distillation and outcome terms
GRPD
None (default settings of the released method)
Dr. OPD
λ=0.4 ; wmin=0.001 ; wmax=3
Appendix
Table 5: Method-specific hyperparameters. All other settings follow Table 4 .
On-policy distillation (OPD) trains a student language model with dense feedback from a stronger teacher on student-generated trajectories. Yet standard OPD weights token-level distillation terms uniformly, implicitly treating local teacher preference as a proxy for correction utility. A decision's task value, however, depends on how the student completes the subsequent reasoning. This mismatch can cause imitation to suppress viable student strategies or reinforce paths the student cannot reliably execute. Verified trajectory outcomes provide complementary evidence about continuation quality, but do not directly identify the utility of individual decisions. We introduce Reward-Aligned Reweighting for On-Policy Distillation (R2-OPD), which uses outcome agreement and the magnitude of teacher--student disagreement to continuously reallocate teacher supervision. It gives reward-aligned corrections greater relative influence while retaining dense feedback, moving beyond uniform imitation and hard filtering. Our analysis formalizes the mismatch between local teacher preference and student continuation value and establishes sufficient conditions for reallocation to improve first-order task progress over uniform OPD. Across seven mathematical reasoning benchmarks, R2-OPD achieves the highest average accuracy among the compared training methods in both cross-size and same-size distillation. It outperforms standard OPD on all seven benchmarks, with average gains of 3.5 and 2.4 percentage points for 1.7B and 4B students, respectively. An extension to code generation yields an average gain of 1.6 percentage points over standard OPD. These results highlight outcome-guided supervision allocation as an effective way to translate dense teacher feedback into stronger student performance across model scales and task domains.
Haofeng Xu, Junwei Su, Lansong Diao +2
The University of Hong Kong · Alibaba Group · University of Science and Technology of China
On-policy distillation (OPD) accelerates post-training by providing dense token-level supervision from a frozen teacher on the student's own rollouts. Vanilla OPD applies this supervision uniformly across prompts, without checking whether the teacher is reliable for each prompt. Because reverse KL is mode-seeking, a confidently wrong teacher can induce a strong yet misleading update. Distributional proxies, such as entropy or teacher-student likelihood agreement, measure uncertainty or agreement but do not directly verify outcome correctness. We introduce Teacher-Gated On-Policy Distillation (TGOPD), built on the principle that teacher reliability should be verified at the prompt level before dense supervision is admitted. TGOPD estimates reliability from a small set of verifier-scored teacher probes and routes each prompt exclusively to dense OPD when the reliability check passes or to verifier-grounded GRPO otherwise. Across 4B and 35B students in mathematics, code, and instruction following, TGOPD outperforms Vanilla OPD in all six single-domain settings and achieves higher seven-benchmark averages at both scales under multi-domain training. By using otherwise-idle teacher capacity for reliability estimation, TGOPD also reduces teacher-side compute waste in asynchronous OPD, increasing teacher-node GPU utilization from 9.8% to 78.9% in the measured 4B single-domain run.
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 \texttt{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.
Yi Ding, Ruqi Zhang
Department of Computer Science, Purdue University, USA