# Stochastic Teacher Intervention for Agentic On-Policy Distillation

arXiv: https://arxiv.org/abs/2610.10878 · HTML: https://mlsanity.com/paper/2610.10878/

## Key facts

- No citing papers in the map yet (data through 7 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 0 of its 44 references that are in the map.
- First posted on arXiv 7 Oct 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- LLM agents and tool use / [Educational agents and math problem solving](https://mlsanity.com/agents/educational-agents-and-math-problem-solving/)

## Abstract (arXiv)

On-policy distillation (OPD) efficiently transfers capabilities from a stronger teacher to a student language model through dense token-level supervision on student-generated rollouts and has shown promise on complex tasks such as mathematical reasoning. However, in multi-turn agentic tasks, student decisions shape subsequent observations, causing early errors to accumulate across turns. The resulting trajectories can drift away from the teacher's rollout distribution, making the teacher's token-level supervision less reliable or even counterproductive for OPD training. To address this issue, we introduce STI-OPD, a stochastic teacher intervention framework for multi-turn agentic OPD. During multi-turn interaction, STI-OPD uses teacher intervention guided by teacher-student policy discrepancy to replace the student's proposed action with a teacher-generated one to maximize the acquisition of reliable supervision. We further develop a stochastic intervention strategy, addressing the limitations of previous threshold-based or fixed-schedule approaches, that estimates policy discrepancy using KL divergence and maps it to an intervention probability. By sampling whether to intervene from this probability, STI-OPD adaptively balances teacher control with student exploration. To learn from the resulting mixed-policy trajectories, we introduce an Importance-Weighted Reverse KL objective that corrects the token sampling mismatch between teacher-generated responses and the student policy to preserve the original OPD objective. Across tool-integrated reasoning and long-horizon interaction, STI-OPD outperforms the strongest prior OPD baseline on every evaluated benchmark and student size. Ablations further show that both discrepancy-guided intervention and importance weighting contribute to these gains.