Persistent Teacher Anchoring for Tool-Using Agents

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) enhances the capabilities of small language agents by providing dense, token-level supervision from a teacher model on student-generated trajectories. However, standard OPD implicitly assumes that credit is uniformly distributed across long-horizon trajectories, assigning the same strength of teacher supervision to different actions. Through credit-distribution analysis and outcome-reversal counterfactual experiments, we find that trajectory credit is concentrated on a small number of critical actions. Moreover, even when the trajectory is held fixed, reversing only the final outcome substantially changes the credit assigned to multiple interaction turns. These findings show that the uniform-credit assumption fails to identify critical decisions and ultimately degrades the model's reasoning accuracy. To address these challenges, we propose ToolOPD, an outcome-aware on-policy distillation framework designed for long-horizon tool use. ToolOPD first summarizes each completed trajectory and its outcome into a reusable hindsight skill. It then measures how this skill changes the teacher's probability of each student action token and converts the change into outcome-aware credit. The resulting credit preserves supervision that supports successful decisions or discourages failed ones, while suppressing irrelevant and conflicting signals. ToolOPD uses these credits to reweight the action-level distillation loss and jointly optimizes it with reinforcement learning. Extensive experiments across multiple long-horizon tool interaction benchmarks demonstrate that ToolOPD significantly outperforms existing reinforcement learning and self-distillation baselines.

Agentic language models must learn when to call tools, when to consume tool responses, and when to answer directly. This makes multi-teacher on-policy distillation a natural training strategy: one teacher can specialize in tool calls, another in direct responses, and the student can learn from both on its own generated distribution. We show that this strategy can induce a behavior shift that is invisible from aggregate losses alone. In a two-teacher tool-use setting, vanilla generalized knowledge distillation improves tool-call recall but also moves the model toward over-calling, where it calls tools on examples that should be answered directly. Aggregate explanations are insufficient: tool-call samples do not receive more token exposure, and full-sequence per-token divergence is not larger for the tool-call teacher. We instead analyze behavior leverage imbalance: local token-level signals at mode- entry and structural positions, such as <tool_call> and function names, can have disproportionate control over the global generation mode. We propose Soft Clamp, a per-token divergence calibration method that dynamically compresses extreme token-level Jensen-Shannon divergence while preserving nonzero gradients. On APIGen-MT, Soft Clamp reduces over-calling from 13.7% to 9.0% relative to vanilla GKD while matching its decision accuracy. In a BFCL multi-turn diagnostic, it also lowers tool-call loops and repeated calls among GKD variants. These results suggest that multi-teacher OPD should monitor where teacher signals act, not only how large they are in aggregate.