Resided at the intersection of multi-fidelity optimization (MFO) and Bayesian optimization (BO), MF BO has found a niche in solving expensive engineering design optimization problems, thanks to its advantages in incorporating physical and mathematical understandings of the problems, saving resources, addressing exploitation-exploration trade-off, considering uncertainty, and processing parallel computing. The increasing number of works dedicated to MF BO suggests the need for a comprehensive review of this advanced optimization technique. In this paper, we survey recent developments of two essential ingredients of MF BO: Gaussian process (GP) based MF surrogates and acquisition functions. We first categorize the existing MF modeling methods and MFO strategies to locate MF BO in a large family of surrogate-based optimization and MFO algorithms. We then exploit the common properties shared between the methods from each ingredient of MF BO to describe important GP-based MF surrogate models and review various acquisition functions. By doing so, we expect to provide a structured understanding of MF BO. Finally, we attempt to reveal important aspects that require further research for applications of MF BO in solving intricate yet important design optimization problems, including constrained optimization, high-dimensional optimization, optimization under uncertainty, and multi-objective optimization.

翻译：位于多保真优化（MFO）与贝叶斯优化（BO）交叉领域的多保真贝叶斯优化（MF BO），凭借其融合问题物理与数学理解、节约资源、平衡探索-利用权衡、考虑不确定性以及支持并行计算等优势，已在解决昂贵工程设计优化问题中占据独特地位。日益增多的MF BO研究工作表明，亟需对该先进优化技术进行全面综述。本文系统梳理了MF BO两大核心要素的最新进展：基于高斯过程（GP）的多保真代理模型与采集函数。首先对现有MF建模方法与MFO策略进行归类，定位MF BO于代理模型优化与MFO算法大家族中的位置；进而利用MF BO各要素方法的共有特性，阐述重要的基于GP的多保真代理模型并评述各类采集函数，以此构建对MF BO的结构化认知。最后，针对MF BO在解决复杂而关键的设计优化问题（包括约束优化、高维优化、不确定性优化及多目标优化）中的应用，揭示亟待深入研究的重点方向。