Bayesian Optimization (BO) is a widely-used method for optimizing expensive-to-evaluate black-box functions. Traditional BO assumes that the learner has full control over all query variables without additional constraints. However, in many real-world scenarios, controlling certain query variables may incur costs. Therefore, the learner needs to balance the selection of informative subsets for targeted learning against leaving some variables to be randomly sampled to minimize costs. This problem is known as Bayesian Optimization with cost-varying variable subsets (BOCVS). While the goal of BOCVS is to identify the optimal solution with minimal cost, previous works have only guaranteed finding the optimal solution without considering the total costs incurred. Moreover, these works assume precise knowledge of the cost for each subset, which is often unrealistic. In this paper, we propose a novel algorithm for the extension of the BOCVS problem with random and unknown costs that separates the process into exploration and exploitation phases. The exploration phase will filter out low-quality variable subsets, while the exploitation phase will leverage high-quality ones. Furthermore, we theoretically demonstrate that our algorithm achieves a sub-linear rate in both quality regret and cost regret, addressing the objective of the BOCVS problem more effectively than previous analyses. Finally, we show that our proposed algorithm outperforms comparable baselines across a wide range of benchmarks.

翻译：贝叶斯优化（BO）是一种广泛用于优化评估代价高昂的黑箱函数的方法。传统BO假设学习者能够完全控制所有查询变量且没有额外约束。然而，在许多实际场景中，控制某些查询变量可能会产生成本。因此，学习者需要在选择信息丰富的子集进行针对性学习与随机采样部分变量以最小化成本之间取得平衡。这一问题被称为具有成本变化变量子集的贝叶斯优化（BOCVS）。虽然BOCVS的目标是以最小成本识别最优解，但先前的研究仅保证了最优解的发现而未考虑产生的总成本。此外，这些研究假设已知每个子集的精确成本，而这往往不切实际。本文针对具有随机未知成本的BOCVS问题扩展提出了一种新颖算法，该算法将过程分为探索与利用两个阶段。探索阶段将筛选掉低质量变量子集，而利用阶段将充分利用高质量子集。进一步，我们从理论上证明了该算法在质量遗憾和成本遗憾上均达到次线性速率，从而比先前分析更有效地解决了BOCVS问题的目标。最后，我们通过大量基准实验表明，所提算法在广泛测试基准上优于可比基线方法。