Cost-aware optimization is a common and important problem in real-world optimizations. Since real-world optimization problems are costly and have no specific mathematical formula, Bayesian optimization (BO) is frequently used to optimize these black-box expensive functions. Typically, a total budget is assigned for BO to find the optimal solution, but how to efficiently use the given budget has not been carefully investigated. In this paper, we propose a single-objective cost-aware BO framework to efficiently optimize an expensive black-box function with regard to the budget. Our proposed method utilizes a multi-armed bandit algorithm to quickly figure out a suitable strategy to deal with the cost of the optimization problem. It is flexible in adapting to different types of optimum-cost relations, extendable to multiple strategies, and simple to implement. We conduct a comprehensive set of experiments on both synthetic and real-world optimization problems to demonstrate the advantages of our method. Experimental results show that our proposed method outperforms other cost-aware BO methods.

成本感知优化是现实世界优化中一个常见且重要的问题。由于现实世界中的优化问题代价高昂且没有特定的数学公式，因此贝叶斯优化 (BO) 经常用于优化这些黑盒代价高昂的函数。通常，为 BO 分配总预算以找到最佳解决方案，但尚未仔细研究如何有效地使用给定的预算。在本文中，我们提出了一个单目标成本感知 BO 框架，以有效地优化与预算相关的昂贵的黑盒函数。我们提出的方法利用多臂老虎机算法来快速找出合适的策略来处理优化问题的成本。灵活适应不同类型的最优成本关系，可扩展到多种策略，并且易于实施。我们对合成和现实世界的优化问题进行了一系列全面的实验，以证明我们方法的优势。实验结果表明，我们提出的方法优于其他成本感知 BO 方法。