Less is More: Early Stopping Rollout for On-Policy Distillation

On-policy distillation (OPD) provides dense teacher feedback along student-generated rollouts rather than fixed teacher traces and has emerged as a promising post-training paradigm. However, standard OPD typically generates full rollouts during training, which is computationally expensive and may expose the student to unreliable teacher feedback at late rollout positions, especially during early training. We identify the rollout horizon as a key bottleneck in OPD that substantially impacts training efficiency. Unlike Reinforcement Learning with Verifiable Rewards (RLVR), OPD does not require a final answer reward to provide learning signals. Therefore, full rollouts may not always be necessary for OPD. Motivated by this insight, we propose two simple horizon-control strategies: Progressive OPD (POPD), which gradually expands the rollout horizon during training, and Truncated OPD (TOPD), which permanently performs distillation on reliable truncated rollouts. Experiments on mathematical reasoning show that POPD improves the training efficiency of OPD by up to 3$\times$, while TOPD matches OPD performance using only 10% of the rollout horizon, leading to substantial wall-clock and memory reductions. These results demonstrate that controlling the rollout horizon offers a simple and practical path to more efficient OPD.

On-Policy Distillation (OPD) improves the learning efficiency of standard reinforcement learning through dense, token-level supervision from teachers. In the standard KL objective of OPD, token-level losses are uniformly averaged, implying equal weights for all tokens. However, we discover that not all tokens are created equal: as student rollouts grow longer, they deviate further from the teacher's distribution, leading to degraded supervision quality at later positions. As a result, OPD using only the first 30% of tokens can perform comparably to using all tokens, whereas OPD using only the last 30% of tokens barely learns anything. In this work, we provide a principled understanding of this issue through the lens of constrained optimization. Based on these insights, we derive Importance-Weighted On-Policy Distillation (IW-OPD), in which the weight assigned to each token depends on the accumulated discrepancy between the student's and teacher's distributions, naturally upweighting earlier tokens and downweighting later ones with larger deviations. We show that IW-OPD converges significantly faster than OPD, with better learning efficiency, and achieves better final performance than standard OPD in both same-size and cross-scale settings, improving performance up to 6.9 points on AIME-2025.

On-policy distillation offers dense, per-token supervision for training reasoning models; however, it remains unclear under which conditions this signal is beneficial and under which it is detrimental. Which teacher model should be used, and in the case of self-distillation, which specific context should serve as the supervisory signal? Does the optimal choice vary from one token to the next? At present, addressing these questions typically requires costly training runs whose aggregate performance metrics obscure the dynamics at the level of individual tokens. We introduce a training-free diagnostic framework that operates at the highest resolution: per token, per question, and per teacher. We derive an ideal per-node gradient defined as the parameter update that maximally increases the student's probability of success. We then develop a scalable targeted-rollout algorithm to estimate this gradient efficiently, even for long chains of intermediate thoughts. The gradient alignment score, defined as the cosine similarity between this ideal gradient and any given distillation gradient, quantifies the extent to which a particular configuration approximates the ideal signal. Across a range of self-distillation settings and external teacher models, we observe that distillation guidance exhibits substantially higher alignment with the ideal on incorrect rollouts than on correct ones, where the student already performs well and the teacher's signal tends to become noisy. Furthermore, we find that the optimal distillation context depends jointly on the student model's capacity and the target task, and that no single universally effective configuration emerges. These findings motivate the use of per-task, per-token diagnostic analyses for distillation.