成本感知多目标老虎机：理论及在预算约束下的大语言模型配置评估中的应用

中文摘要 AI 辅助

大语言模型（LLM）配置评估存在挑战，原因在于评估预算有限、成本各异且存在多个相互竞争的目标。本文将LLM配置评估建模为成本感知多目标老虎机问题，其中每次配置评估会产生与配置相关的成本，并输出带噪声的向量值结果。在该框架下，我们研究两个基本问题：在线配置选择和帕累托配置识别。针对在线配置选择，我们提出一种基于超体积的UCB算法，该算法优化乐观超体积-成本指标。我们证明其预算相关的遗憾界为$O\bigl(\sum_{i\ne i^\star}\frac{\log B}{\Delta_i}\bigr)$，其中$B$为评估预算，$i^\star$为超体积效率最优的配置，$\Delta_i$为配置$i$对应的效率差距。该遗憾界保留了经典单目标预算老虎机的对数预算依赖性。针对固定预算下的帕累托识别，我们开发了一种成本感知经验差距消除算法，并证明其误差概率为$O\bigl(\exp(-\frac{B}{H_{\mu,c}})\bigr)$，其中$H_{\mu,c}$为依赖于配置成本和帕累托分类差距的成本感知帕累托识别复杂度。该误差概率随评估预算指数衰减，且当所有配置成本相同时，可恢复标准帕累托集识别保证。在LLM配置评估任务上的实验表明，所提框架能在有限预算下实现高效在线决策和准确的成本感知帕累托识别。

英文摘要

Large language model (LLM) configuration evaluation is challenging due to limited evaluation budgets, varying costs, and multiple competing objectives. In this paper, we formulate LLM configuration evaluation as a cost-aware multi-objective bandit problem, where each configuration evaluation incurs a configuration-dependent cost and yields a noisy vector-valued outcome. Under this framework, we study two fundamental problems: online configuration selection and Pareto configuration identification. For online configuration selection, we propose a hypervolume-based UCB algorithm that optimizes an optimistic hypervolume-per-cost index. We establish a budgeted regret bound of order $O\bigl(\sum_{i\ne i^\star}\frac{\log B}{Δ_i}\bigr)$, where $B$ is the evaluation budget, $i^\star$ is the optimal configuration in terms of hypervolume efficiency, and $Δ_i$ is the corresponding efficiency gap of configuration $i$. This bound retains the logarithmic budget dependence of classical single-objective budgeted bandits. For fixed-budget Pareto identification, we develop a cost-aware empirical gap elimination algorithm and prove that its error probability is of order $O\bigl(\exp(-\frac{B}{H_{μ,c}})\bigr)$, where $H_{μ,c}$ is a cost-aware Pareto identification complexity depending on configuration costs and Pareto classification gaps. This error probability decays exponentially with the evaluation budget and recovers the standard Pareto set identification guarantee when all configuration costs are identical. Experiments on LLM configuration evaluation tasks demonstrate that the proposed framework enables efficient online decision-making and accurate cost-aware Pareto identification under limited budgets.

发表机构

• City University of Hong Kong（香港城市大学）
• South China University of Technology（华南理工大学）
• Zhejiang University（浙江大学）

机构由 AI 辅助整理，请以论文原文为准。