ReOPD turns expensive agent-environment interaction into a reusable offline resource, enabling scalable distillation across tools, tasks, and environments and preserves or improves OPD-level accuracy, uses zero tool calls during student training, and is at least 4$\times faster per rollout than OPD.
Abstract
We study on-policy distillation (OPD) for agentic tasks, where an LLM agent interacts with an environment over multiple turns and a student imitates a teacher over these multi-turn interaction histories. Fully online OPD is costly because each update requires fresh student rollouts through the environment and teacher queries at visited histories. We propose Replayed-Prefix On-Policy Distillation (ReOPD), an off-environment alternative that reuses pre-collected teacher trajectories as replayed prefixes: the student acts at selected steps, while the teacher provides dense per-step supervision without executing new environment interactions. We show that multi-turn OPD introduces a prefix trap: making histories more student-on-policy improves relevance to the student, but can query the teacher on histories where its target is unreliable. This creates a two-sided distribution shift between student occupancy and teacher reliability. ReOPD addresses this by treating multi-turn OPD as a reliability-aware prefix distribution design and implements it with a simple step-decaying sampling schedule that emphasizes early, lower-shift prefixes. Across mathematical reasoning with Python and search environments over multiple teacher and student model scales, ReOPD preserves or improves OPD-level accuracy, uses zero tool calls during student training, and is at least 4$\times$ faster per rollout than OPD. ReOPD therefore turns expensive agent-environment interaction into a reusable offline resource, enabling scalable distillation across tools, tasks, and environments.
Distillation is common in LLM post-training, where on-policy knowledge distillation (OPKD) uses student-generated trajectories to prepare the student for downstream RL. At each state, the student matches a next-token distribution supplied by the teacher. As the rollout enters states the teacher would not visit, the teacher-student distribution gap can accumulate. In tool use, this gap becomes consequential because student-written calls execute before supervision and their observations shape later prefixes. Proposer-verifier generation addresses this drift by letting the teacher decide which student-proposed text is retained during generation. Existing formulations govern text but leave tool execution outside their scope. We propose Persistent Teacher Anchoring (PTA), a student-induced but teacher-committed rollout construction. PTA retains chunk-level verification and adds turn-level commitment, allowing a call to reach the environment only after the teacher has verified the entire turn. Treating verified chunks as atomic generation units, we introduce persistent lookahead, which fills idle rollout capacity by advancing future samples and carrying unfinished ones across student updates under the fixed verifier. Across Search-R1-style retrieval and DeepEyes-style perception RL, applying PTA before downstream RL improves macro best@4 by 2.5 and 2.8 points over OPKD under the same downstream RL budget, while lookahead improves throughput by 24%.
Hyung Bin Park, Kyung-dong Song, Sang-Min Lee et al.· 0 citations
While on-policy distillation (OPD) reduces exposure bias by training student language models on their own rollouts, early student errors in long-horizon agentic scenarios can lead to contexts unfamiliar to the teacher. To improve trajectory quality, recent work on agentic OPD introduces teacher intervention into training rollouts by switching the executor between the student and the teacher. However, existing methods determine how much teacher intervention is needed---but not when. To address this limitation, we propose DASH-OPD (Discrepancy-Aware Switching with Hysteresis for OPD), the first agentic OPD method to perform adaptive, bidirectional executor switching. At each turn, DASH-OPD measures teacher--student discrepancy using a mean log-probability ratio over action tokens. Student-to-teacher ratios on student turns serve as drift signals, while teacher-to-student ratios on teacher turns serve as recovery signals. These signals are accumulated over multiple turns to form drift and recovery evidence, respectively. DASH-OPD switches executors when either type of evidence exceeds its corresponding switching threshold, introducing hysteresis that prevents rapid switching triggered by transient discrepancy fluctuations. Across three benchmarks and two student model sizes, DASH-OPD outperforms five baselines in all 14 task performance comparisons, while requiring the fewest interaction turns in nine of ten efficiency comparisons. Code, models, and training logs are available at https://github.com/Lucian1115/DASH-OPD
Yuchen Xia, Qianguo Sun, Chao Song et al.· arXiv.org· 0 citations
WDL-OPD is introduced, a mixture-constrained co-training method with two trainable policies that shows that freezing the auxiliary recovers an anchor-plus-contrast proxy target closely related to OPD$^2$ and W2S-OPD, whereas joint training creates branch-level degrees of freedom that a static delta cannot express.
Zehao Chen, Gong-Xun Li, Tianxiang Ai et al.· 0 citations
Self-OPD is introduced, a teacher-free OPD framework for flow matching models that turns the student's own self-exploration into step-wise supervision and outperforms prior RL and OPD methods without task-specific teachers.
Shiyi Zhang, Mu-Shui Liu, Yunze Tong et al.· 0 citations
Privileged on-policy distillation provides dense supervision for multi-turn agents by allowing a synchronized teacher to re-score the student's response at every turn with access to training-only references, such as successful trajectories. In interactive environments, however, the student's preceding actions continually change the execution state. As the student takes different actions or completes subgoals in a different order, its rollout may reach states not covered by the reference, making the reference an unreliable source of guidance for the state actually reached. Applying privileged distillation indiscriminately therefore creates state--reference mismatch. This mismatch motivates a central objective: providing privileged reference guidance that remains compatible with the student's current execution state. We introduce State-Matched Routing and Contextualized Self-Distillation (SMRC-SD), which explicitly determines when and how a privileged trajectory should guide an on-policy student. At each turn, SMRC-SD verifies whether the student's current execution state matches a supported state along the reference trajectory. Distillation is applied only at matched states, filtering out turns for which the reference lacks locally compatible guidance. For each matched state, SMRC-SD further constructs state-conditioned teacher context from the successful trajectory, grounding supervision in the state actually reached. Across ALFWorld and WebShop, SMRC-SD consistently outperforms unconditional successful full-path distillation. With Qwen3-1.7B, it improves task success from $0.746$ to $0.865$ on ALFWorld and from $0.574$ to $0.693$ on WebShop. Controlled routing and context ablations support both selecting locally supported turns and constructing state-compatible teacher context as contributors to these gains. Code is available at https://github.com/liujunzhuo/SMRC-SD.
Junzhuo Liu, Weiwei Li, Jun Ling et al.· 0 citations
This work introduces a student reference KL loss and mask the advantages of special termination tokens to mitigate the problem of excessive generation length and frequent truncation, and improves on science benchmarks such as HLE and HiPhO, suggesting that OPD transfers reasoning capabilities that generalize beyond the mathematical training domain.
Haonan He, Hao Lei, Yun Luo et al.· 3 citations· ⚡1
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