Optimal Budgeted Adaptation of Large Language Models

• URL: http://arxiv.org/abs/2602.00952v1
• Date: Sun, 01 Feb 2026 01:08:15 GMT
• Title: Optimal Budgeted Adaptation of Large Language Models
• Authors: Jing Wang, Jie Shen, Dean Foster, Zohar Karnin, Jeremy C Weiss,
• Abstract summary: Trade-off between labeled data availability and downstream accuracy remains a central challenge in large language models.<n>We propose a principled framework for emphbudget-aware supervised fine-tuning by casting LLM adaptation as a contextual Stackelberg game.
• Score: 8.207283283207138
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 \emph{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 $\tilde{O}(d\sqrt{T})$ 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 $\tilde{O}(\sqrt{dB} + c\sqrt{B})$ with $B=βT$.

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