# Teaching Agents in their Own Style: Blackbox Teacher Distillation for Web Agents

arXiv: https://arxiv.org/abs/2610.19834 · HTML: https://mlsanity.com/paper/2610.19834/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Educational agents and math problem solving, one of 16 directions in LLM agents and tool use.
- Builds on 34 of its 42 references that are in the map.
- First posted on arXiv 14 Oct 2026.

## Placed in

- LLM agents and tool use / [Educational agents and math problem solving](https://mlsanity.com/agents/educational-agents-and-math-problem-solving/)

## Builds on (most cited first, 30 of 34)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [OpenVLA: An Open-Source Vision-Language-Action Model](https://mlsanity.com/paper/2406.09246/) (2024)
- [WebArena: A Realistic Web Environment for Building Autonomous Agents](https://mlsanity.com/paper/2307.13854/) (2023)
- [Mind2Web: Towards a Generalist Agent for the Web](https://mlsanity.com/paper/2306.06070/) (2023)
- [OSWorld: Benchmarking Multimodal Agents for Open-Ended Tasks in Real Computer Environments](https://mlsanity.com/paper/2404.07972/) (2024)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [WebVoyager: Building an End-to-End Web Agent with Large Multimodal Models](https://mlsanity.com/paper/2401.13919/) (2024)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [Gemma 4 Technical Report](https://mlsanity.com/paper/2607.02770/) (2026)
- [WebRL: Training LLM Web Agents via Self-Evolving Online Curriculum Reinforcement Learning](https://mlsanity.com/paper/2411.02337/) (2024)
- [DigiRL: Training In-The-Wild Device-Control Agents with Autonomous Reinforcement Learning](https://mlsanity.com/paper/2406.11896/) (2024)
- [An Illusion of Progress? Assessing the Current State of Web Agents](https://mlsanity.com/paper/2504.01382/) (2025)
- [WebAgent-R1: Training Web Agents via End-to-End Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2505.16421/) (2025)
- [DistiLLM: Towards Streamlined Distillation for Large Language Models](https://mlsanity.com/paper/2402.03898/) (2024)
- [The BrowserGym Ecosystem for Web Agent Research](https://mlsanity.com/paper/2412.05467/) (2024)
- [Is Your LLM Secretly a World Model of the Internet? Model-Based Planning for Web Agents](https://mlsanity.com/paper/2411.06559/) (2024)
- [OpenWebVoyager: Building Multimodal Web Agents via Iterative Real-World Exploration, Feedback and Optimization](https://mlsanity.com/paper/2410.19609/) (2024)
- [BEARCUBS: A benchmark for computer-using web agents](https://mlsanity.com/paper/2503.07919/) (2025)
- [Better than Your Teacher: LLM Agents that learn from Privileged AI Feedback](https://mlsanity.com/paper/2410.05434/) (2024)
- [Imitation Learning for Multi-turn LM Agents via On-policy Expert Corrections](https://mlsanity.com/paper/2512.14895/) (2025)
- [WebCoT: Enhancing Web Agent Reasoning by Reconstructing Chain-of-Thought in Reflection, Branching, and Rollback](https://mlsanity.com/paper/2505.20013/) (2025)
- [On-Policy Self-Distillation without Any Supervision](https://mlsanity.com/paper/2608.06296/) (2026)
- [I Learn Better If You Speak My Language: Understanding the Superior Performance of Fine-Tuning Large Language Models with LLM-Generated Responses](https://mlsanity.com/paper/2402.11192/) (2024)

## Abstract (arXiv)

Frontier web agents using closed models have high inference and computational costs. Smaller open models can be an alternative, but to be performant, they require training supervision from a human or teacher model. Token-level teacher distillation is not an option for closed teachers as it needs access to the model's logits. The standard approach is to imitate teacher demonstrations offline, but it trains the student on states it has never visited, and in a style it does not write in. We introduce WebKD, where the teacher is the editor of the student's failures. Given a failed episode, the teacher finds the first point of mistake, and rewrites the student's reasoning traces, harness states, and actions from that point onward. The editing reveals that the teacher's corrections can be more surprising to the student than the student's own text. WebKD instead aims to edit minimally. In the data space, the teacher writes each correction in the student's style. In the objective space, the reasoning is weighted by its contribution to the action. A role-asymmetric KL anchor allows the corrected action to move freely while keeping the reasoning near the student's prior. On the TimeWarp benchmark, WebKD students gain about 5.5-10.7 pp over behavior cloning, outcome-reward RL, and teacher editing baselines. The performance transfers to unseen versions and to the live web in the OnlineMind2Web benchmark. WebKD opens a new way of distilling black-box models to improve the capabilities of open-weight web agents.