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：多保真度贝叶斯优化（MF BO）融合了多保真度优化（MFO）与贝叶斯优化（BO）的优势，在解决昂贵的工程设计优化问题中展现出独特价值。其优势在于能够整合问题的物理与数学理解、节约计算资源、平衡探索与利用、处理不确定性以及支持并行计算。随着MF BO相关研究的快速增长，对这一先进优化技术进行全面综述的需求日益凸显。本文系统回顾了MF BO两个核心组成部分的最新进展：基于高斯过程（GP）的多保真度代理模型与采集函数。我们首先对现有多保真度建模方法与MFO策略进行分类，将MF BO置于基于代理模型的优化与MFO算法大家族中进行定位。进而通过分析MF BO各组成部分方法的共性特征，详细阐述了重要的GP基多保真度代理模型，并综述了各类采集函数的发展。通过这种结构化分析，我们期望为MF BO提供系统化的理解框架。最后，我们尝试揭示MF BO在解决复杂而重要的设计优化问题（包括约束优化、高维优化、不确定性条件下的优化以及多目标优化）时需要进一步深入研究的关键方向。