# Teacher-Guided Policy Optimization for On-Policy Reasoning Distillation under Large Policy Divergence

arXiv: https://arxiv.org/abs/2605.13230 · HTML: https://mlsanity.com/paper/2605.13230/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 17 of its 29 references that are in the map.
- First posted on arXiv 13 May 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)
- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Builds on (most cited first, 17 of 17)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [MiMo-V2-Flash Technical Report](https://mlsanity.com/paper/2601.02780/) (2026)
- [Skywork Open Reasoner 1 Technical Report](https://mlsanity.com/paper/2505.22312/) (2025)
- [MiniLLM: On-Policy Distillation of Large Language Models](https://mlsanity.com/paper/2306.08543/) (2023)
- [On-Policy RL Meets Off-Policy Experts: Harmonizing Supervised Fine-Tuning and Reinforcement Learning via Dynamic Weighting](https://mlsanity.com/paper/2508.11408/) (2025)
- [No Prompt Left Behind: Exploiting Zero-Variance Prompts in LLM Reinforcement Learning via Entropy-Guided Advantage Shaping](https://mlsanity.com/paper/2509.21880/) (2025)
- [KDRL: Post-Training Reasoning LLMs via Unified Knowledge Distillation and Reinforcement Learning](https://mlsanity.com/paper/2506.02208/) (2025)

## Built on by (most cited first, 13 of 13)

- [Mismatch Matters: On-Policy Distillation Beyond Token Agreement](https://mlsanity.com/paper/2608.09836/) (2026)
- [PowerOPD: Stabilizing On-Policy Distillation with Bounded Power Transformation](https://mlsanity.com/paper/2606.17199/) (2026)
- [A Formula-Driven Survey and Research Agenda for On-Policy Distillation](https://mlsanity.com/paper/2606.22793/) (2026)
- [OPDSearch+: On-Policy Distillation with RL Refinement for Search-Augmented Reasoning](https://mlsanity.com/paper/2608.24310/) (2026)
- [TISD: On-Policy Self-Distillation with Trajectory Intervention](https://mlsanity.com/paper/2609.30878/) (2026)
- [Expected Reasoning-Step Return Unifies On-Policy Learning from Rewards and Teachers](https://mlsanity.com/paper/2609.32674/) (2026)
- [TIDE: Teacher-Student Transition via Informative Distillation and Exploration for Agentic RL](https://mlsanity.com/paper/2609.35058/) (2026)
- [Improving OCR Faithfulness via Gated and Attenuated On-Policy Distillation](https://mlsanity.com/paper/2609.38282/) (2026)
- [From Given to Gathered Evidence: Agentic Learning for Longitudinal Medical Reasoning](https://mlsanity.com/paper/2609.39566/) (2026)
- [DiffGate: Difficulty-Gated Teacher Guidance for On-Policy Distillation](https://mlsanity.com/paper/2610.04596/) (2026)
- [PIVOT: Perplexity-Informed KD-to-RL Transition Scheduling for Vertical-Domain Few-Shot Distillation](https://mlsanity.com/paper/2610.11167/) (2026)
- [Demystifying On-Policy Distillation: Where Does the Teacher's Advantage Live?](https://mlsanity.com/paper/2610.19145/) (2026)
- [DTDD: Divergence-Triggered Dynamic Distillation for Reliable On-Policy Supervision](https://mlsanity.com/paper/2610.19302/) (2026)

## Abstract (arXiv)

On-policy distillation (OPD) has become a promising paradigm for reasoning-oriented post-training of large language models (LLMs), especially when combined with reinforcement learning from verifiable rewards (RLVR). Existing OPD methods rely on reverse KL (RKL)-based teacher supervision over trajectories sampled from the student policy. However, we identify a critical limitation: under large teacher--student policy divergence, RL-driven exploration often produces trajectories outside the teacher distribution, resulting in uninformative negative feedback. To address this, we propose Teacher-Guided Policy Optimization (TGPO), an on-policy reasoning distillation method that remains effective under large policy divergence settings. Rather than relying solely on evaluative supervision, TGPO uses teacher to directly guide token level generation conditioning on student-generated contexts; together with RLVR-style trajectory level rewards, TGPO steers exploration toward improved continuations. Experiments on reasoning benchmarks show that TGPO consistently outperforms existing RKL-based OPD methods and remains robust across different teacher models.