MAD-OPD: Breaking the Ceiling in On-Policy Distillation via Multi-Agent Debate

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$\times$ 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.

On-policy distillation (OPD) has shown strong potential for transferring reasoning ability from frontier or domain-specific models to smaller students. While effective on static single-turn tasks, its behavior in multi-turn agent settings remains underexplored. In this work, we identify a key limitation of vanilla OPD in such settings, which we term Trajectory-Level KL Instability. Specifically, we observe that KL divergence increases together with a drop in success rate, and even after convergence, the KL remains high, leading to unstable training. This instability arises from inter-turn error compounding: as errors accumulate, the student is driven beyond the teacher's effective support, rendering the supervision signal unreliable. To address this, we propose TCOD (Temporal Curriculum On-Policy Distillation), a simple yet effective framework that controls the trajectory depth exposed to the student and progressively expands it from short to long with a curriculum schedule. Experimental results across four student-teacher pairs on three multi-turn agent benchmarks (ALFWorld, WebShop, ScienceWorld) show that TCOD mitigates KL escalation and enhances KL stability throughout training, improving agent performance by up to 18 points over vanilla OPD. Further evaluations show that TCOD can even surpass the teacher's performance and generalize to tasks on which the teacher fails. Our code is available at https://github.com/kokolerk/TCOD.