In reinforcement learning for multi-turn agents, a sparse outcome reward makes credit assignment across intermediate tool calls difficult. On-policy self-distillation eases credit assignment by having the model teach itself with dense supervision: the model with privileged information (the teacher) scores each token generated by the model without it (the student). However, it remains unclear what forms of feedback are most effective in multi-turn agentic settings. We find that the natural multi-turn variant fails: when the teacher is given a complete successful demonstration at every turn, training makes the agent worse than the untrained model. The teacher ends up rewarding the student for copying the demonstration, even when a copied action is not right in the student's context. We propose HINT, in which a reflector, by default the policy itself, reads the completed trajectory and writes short turn-level feedback. The teacher then sees what went wrong at each turn, not the actions that followed. On Tau-Bench and WebShop, HINT matches GRPO with one-eighth as many rollouts.

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