# A Good Self-Teacher Meets the Student Where They Are: Joint On-Policy Learning and Teaching

arXiv: https://arxiv.org/abs/2610.10447 · HTML: https://mlsanity.com/paper/2610.10447/

## Key facts

- No citing papers in the map yet (data through 7 Oct 2026).
- Builds on 39 of its 48 references that are in the map.
- First posted on arXiv 7 Oct 2026.

## Builds on (most cited first, 30 of 39)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [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)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [Deep Reinforcement Learning at the Edge of the Statistical Precipice](https://mlsanity.com/paper/2108.13264/) (2021)
- [Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1910.00177/) (2019)
- [Terminal-Bench: Benchmarking Agents on Hard, Realistic Tasks in Command Line Interfaces](https://mlsanity.com/paper/2601.11868/) (2026)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [Maximum a Posteriori Policy Optimisation](https://mlsanity.com/paper/1806.06920/) (2018)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [On-Policy Context Distillation for Language Models](https://mlsanity.com/paper/2602.12275/) (2026)
- [Learning beyond Teacher: Generalized On-Policy Distillation with Reward Extrapolation](https://mlsanity.com/paper/2602.12125/) (2026)
- [Entropy-Aware On-Policy Distillation of Language Models](https://mlsanity.com/paper/2603.07079/) (2026)
- [A Survey of On-Policy Distillation for Large Language Models](https://mlsanity.com/paper/2604.00626/) (2026)
- [Learning by Distilling Context](https://mlsanity.com/paper/2209.15189/) (2022)
- [Revisiting On-Policy Distillation: Empirical Failure Modes and Simple Fixes](https://mlsanity.com/paper/2603.25562/) (2026)
- [Self-Distilled RLVR](https://mlsanity.com/paper/2604.03128/) (2026)
- [The Art of Scaling Reinforcement Learning Compute for LLMs](https://mlsanity.com/paper/2510.13786/) (2025)
- [Why Does Self-Distillation (Sometimes) Degrade the Reasoning Capability of LLMs?](https://mlsanity.com/paper/2603.24472/) (2026)
- [Privileged Information Distillation for Language Models](https://mlsanity.com/paper/2602.04942/) (2026)
- [Skill-SD: Skill-Conditioned Self-Distillation for Multi-turn LLM Agents](https://mlsanity.com/paper/2604.10674/) (2026)
- [ProgramBench: Can Language Models Rebuild Programs From Scratch?](https://mlsanity.com/paper/2605.03546/) (2026)

## Abstract (arXiv)

Reinforcement Learning (RL) from outcome rewards suffers from sparse supervision, particularly on difficult, long-horizon tasks where successful trajectories are rare and costly to generate. On-Policy Distillation (OPD) offers an attractive alternative by providing dense token-level supervision from a stronger teacher along the student's own generations. Self-distillation methods further remove the need for a separate teacher model by conditioning the same policy on privileged information to serve as its own teacher. However, privileged conditioning alone does not guarantee that the resulting distillation update improves the student. Indeed, privileged information can lead the teacher to solve tasks through shortcuts unavailable to the student, producing supervision poorly matched to the student's current behavior. Consequently, even a higher-performing teacher can provide guidance that degrades student performance. To address this, we analyze how the choice of privileged teacher affects the student's update. We derive a necessary and sufficient condition for the teacher's local distillation update to be a positive multiple of the student's reward gradient. Our analysis suggests that the teacher should not only perform well on the task, but also provide guidance suited to the student's current capabilities. This characterization motivates a practical teacher-training surrogate that combines outcome rewards with token-level Kullback-Leibler (KL) regularization toward the student. Based on this result, we propose Joint On-Policy Learning and Teaching (JOLT), which jointly trains a single policy in two roles: a privileged teacher using a KL-regularized objective, and an unprivileged student using dense on-policy distillation. Across mathematical reasoning, coding, tool use, and terminal use, JOLT improves training efficiency and performance, with further gains from student rewards.