Does On-Policy Distillation Need to Complete Every Rollout?

On-policy distillation (OPD) has become increasingly popular for transferring teacher capabilities to student models. In this work, we ask a critical research question: Is on-policy sampling always beneficial for distilling arbitrary teacher-student pairs? We show that a simple alternative, Semi-OPD, which distills from offline rollouts generated by the initial student, can often outperform OPD in both accuracy and training efficiency. Across 17 teacher-student pairs ranging from 1.5B to 235B parameters, Semi-OPD outperforms OPD in 14 cases, with up to +13.6% accuracy and 11.4x training speedup. We further find that the choice between OPD and Semi-OPD depends on the alignment between the initial teacher and student, quantified by an output-token overlap ratio: OPD is beneficial only when the two are highly aligned with high overlap ratios. Our deeper investigation suggests that effective distillation requires on-policyness w.r.t. both the student and the teacher. For misaligned pairs, student rollouts can become increasingly off-policy w.r.t. the teacher as context length grows, weakening the distillation signal. In contrast, Semi-OPD is often more stable, as it distills on shorter contexts while covering full trajectories and exposing the student to more teacher-preferred tokens. Beyond proposing Semi-OPD as an efficient alternative, our work motivates the community to rethink when to use OPD and to study stronger OPD variants with meaningful teacher-student pairs.

On-policy distillation (OPD) improves language-model post-training by letting the student learn from its own sampled trajectories under teacher supervision, aligning the training process with inference-time behavior. However, the rollout policy in OPD is usually treated as fixed: each round samples directly from the current student. We show that this choice can create a compounding teacher--student mismatch, because it requires the teacher to provide effective supervision on whichever trajectories the student samples, including ones less reachable by the teacher itself. On such trajectories, teacher supervision can become noisy or even misleading, leading to undesirable student patterns such as repetition. Moreover, since the updated student in turn defines the rollout policy of subsequent rounds, these patterns persist and potentially amplify over training. This failure mode suggests that improving OPD requires treating the rollout policy itself as an optimization target, rather than only modifying the distillation objective. We propose Mixture Proposal On-Policy Distillation (MPOPD), which derives a student-anchored, teacher-guided rollout distribution from a local trust-region objective based on relative teacher support. The resulting target is a geometric mixture of the student and teacher policies, and we introduce a proposal policy that approximates this mixture, enabling rollout generation in a single forward pass. Experiments on 16 math, knowledge, and medical reasoning benchmarks show consistent gains over OPD and recent variants. On math reasoning, our method improves average accuracy by 6.91 over OPD on Qwen3-4B-Base while reducing average generation length by 41%, suggesting that rollout policy design provides an effective way to improve OPD.

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.