# When and What to Teach: Budget-Aware Online Adaptation for Web Agents

arXiv: https://arxiv.org/abs/2609.05513 · HTML: https://mlsanity.com/paper/2609.05513/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use.
- Builds on 35 of its 50 references that are in the map.
- First posted on arXiv 31 Aug 2026.

## Placed in

- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 30 of 35)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [WebArena: A Realistic Web Environment for Building Autonomous Agents](https://mlsanity.com/paper/2307.13854/) (2023)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [WebShop: Towards Scalable Real-World Web Interaction with Grounded Language Agents](https://mlsanity.com/paper/2207.01206/) (2022)
- [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)
- [SimPO: Simple Preference Optimization with a Reference-Free Reward](https://mlsanity.com/paper/2405.14734/) (2024)
- [ExpeL: LLM Agents Are Experiential Learners](https://mlsanity.com/paper/2308.10144/) (2023)
- [Approximate Nearest Neighbor Negative Contrastive Learning for Dense Text Retrieval](https://mlsanity.com/paper/2007.00808/) (2020)
- [Training Region-based Object Detectors with Online Hard Example Mining](https://mlsanity.com/paper/1604.03540/) (2016)
- [Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models](https://mlsanity.com/paper/2401.01335/) (2024)
- [DoReMi: Optimizing Data Mixtures Speeds Up Language Model Pretraining](https://mlsanity.com/paper/2305.10429/) (2023)
- [Reinforcement Learning on Web Interfaces Using Workflow-Guided Exploration](https://mlsanity.com/paper/1802.08802/) (2018)
- [Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMs](https://mlsanity.com/paper/2406.18629/) (2024)
- [HG-DAgger: Interactive Imitation Learning with Human Experts](https://mlsanity.com/paper/1810.02890/) (2018)
- [Direct Language Model Alignment from Online AI Feedback](https://mlsanity.com/paper/2402.04792/) (2024)
- [Prioritized Training on Points that are Learnable, Worth Learning, and Not Yet Learnt](https://mlsanity.com/paper/2206.07137/) (2022)
- [WebAgent-R1: Training Web Agents via End-to-End Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2505.16421/) (2025)
- [The BrowserGym Ecosystem for Web Agent Research](https://mlsanity.com/paper/2412.05467/) (2024)
- [ThriftyDAgger: Budget-Aware Novelty and Risk Gating for Interactive Imitation Learning](https://mlsanity.com/paper/2109.08273/) (2021)
- [Watch Every Step! LLM Agent Learning via Iterative Step-Level Process Refinement](https://mlsanity.com/paper/2406.11176/) (2024)
- [Query-Efficient Imitation Learning for End-to-End Autonomous Driving](https://mlsanity.com/paper/1605.06450/) (2016)
- [Perplexed by Perplexity: Perplexity-Based Data Pruning With Small Reference Models](https://mlsanity.com/paper/2405.20541/) (2024)
- [Direct Multi-Turn Preference Optimization for Language Agents](https://mlsanity.com/paper/2406.14868/) (2024)

## Abstract (arXiv)

Web agents have achieved significant success in automating complex internet tasks but deploying them in real-world environments requires continuous online adaptation. Given that deploying powerful proprietary models remains commercially cost-prohibitive, practitioners must rely on lightweight local models that evolve post-deployment via online teaching from a stronger teacher. However, standard interactive feedback imposes prohibitive costs. We show that conventional trajectory-level preference optimization wastes budget on both unresolvable episodes and redundant execution turns. To resolve these inefficiencies, we propose Score-Guided Online Teaching with Budgeted Trajectory Trimming, a budget-aware framework that systematically orchestrates when and what to teach. Specifically, our framework integrates a solvability-aware teacher gate to dictate when to query the teacher model and a score-guided turn selection mechanism to decide what informative turns to retain. Extensive experiments on MiniWoB and TimeWarp demonstrate that our method achieves comparable first-pass success while reducing teacher calls by 22.6% and student training compute by 52.1% on average. Our code is available at https://github.com/zjw131f1fc/budgeted-online-teaching.