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.
Multi-turn agents that plan, invoke tools, and interact with environments offer a promising paradigm for solving complex tasks, yet their capabilities typically rely on very large models whose inference cost is prohibitive in practice. On-Policy Distillation (OPD) is a natural recipe for transferring such capabilities to smaller students, but we find that it suffers a characteristic failure mode in this setting: small student errors compound across turns and push the trajectory out of the teacher's familiar state distribution, so the teacher's supervision becomes least reliable precisely where the student needs it most. We propose Guided On-Policy Distillation (Guided-OPD), a simple yet effective algorithm that mixes teacher- and student-generated turns within each rollout and schedules the teacher's intervention probability along a curriculum that decays to zero. Strong guidance keeps early trajectories close to the teacher distribution and is then gradually withdrawn to recover the purely on-policy regime used at inference. On ALFWorld, ScienceWorld, and WebShop, distilling Qwen3 students from a Qwen3-30B-A3B teacher, Guided-OPD yields average relative gains of 21.1% in Score and 25.5% in Success Rate over vanilla OPD, with larger gains on smaller students.
On-policy distillation (OPD) provides teacher supervision on states visited by the student, reducing the distribution gap between training and inference. However, in multi-turn agentic tasks, student deviations may accumulate over time, gradually moving the trajectory away from states where teacher guidance remains effective. Our quantitative analysis further shows that high-disagreement states offer promising opportunities for teacher guidance, but determining whether such guidance is beneficial requires examining its effect on subsequent student trajectories. We propose FutureBridge-OPD (FTB), which executes a short teacher bridge at a high disagreement state and uses the resulting student continuation to assess whether the bridge increases the density of positive distillation signals relative to the teacher. On ALFWorld, WebShop, and ScienceWorld, under the main Qwen3-32B teacher to Qwen3-1.7B student setting, FTB outperforms vanilla OPD and TCOD by an average of 16.6 and 7.6 points, respectively, and remains effective across student scales and teacher settings. Our code is publicly available at https://github.com/ChenChiShui/FutureBridge-OPD.
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× 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.