# Optimal Budgeted Adaptation of Large Language Models

arXiv: https://arxiv.org/abs/2602.00952 · HTML: https://mlsanity.com/paper/2602.00952/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 33 references that are in the map.
- First posted on arXiv 1 Feb 2026.

## Builds on (most cited first, 14 of 14)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [What Disease does this Patient Have? A Large-scale Open Domain Question Answering Dataset from Medical Exams](https://mlsanity.com/paper/2009.13081/) (2020)
- [Towards a Unified View of Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2110.04366/) (2021)
- [Knowledge Neurons in Pretrained Transformers](https://mlsanity.com/paper/2104.08696/) (2021)
- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [The Statistical Complexity of Interactive Decision Making](https://mlsanity.com/paper/2112.13487/) (2021)
- [Online Learning in Stackelberg Games with an Omniscient Follower](https://mlsanity.com/paper/2301.11518/) (2023)
- [Decentralized Cooperative Reinforcement Learning with Hierarchical Information Structure](https://mlsanity.com/paper/2111.00781/) (2021)
- [Attribute-Efficient Learning of Halfspaces with Malicious Noise: Near-Optimal Label Complexity and Noise Tolerance](https://mlsanity.com/paper/2006.03781/) (2020)
- [Sample-Optimal PAC Learning of Halfspaces with Malicious Noise](https://mlsanity.com/paper/2102.06247/) (2021)
- [Regret Minimization in Stackelberg Games with Side Information](https://mlsanity.com/paper/2402.08576/) (2024)
- [Nearly-Optimal Bandit Learning in Stackelberg Games with Side Information](https://mlsanity.com/paper/2502.00204/) (2025)

## Abstract (arXiv)

The trade-off between labeled data availability and downstream accuracy remains a central challenge in fine-tuning large language models (LLMs). We propose a principled framework for budget-aware supervised fine-tuning by casting LLM adaptation as a contextual Stackelberg game. In our formulation, the learner (leader) commits to a scoring policy and a label-querying strategy, while an adaptive environment (follower) selects challenging supervised alternatives in response. To explicitly address label efficiency, we incorporate a finite supervision budget directly into the learning objective. Our algorithm operates in the full-feedback regime and achieves tildeO(d√T) regret under standard linear contextual assumptions. We extend the framework with a Largest-Latency-First (LLF) confidence gate that selectively queries labels, achieving a budget-aware regret bound of tildeO(√dB + c√B) with B=β T.