Multifidelity Bayesian Optimization: A Review

Resided at the intersection of multifidelity 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. This paper surveys recent developments of two essential ingredients of MF BO: Gaussian process (GP) based MF surrogates and acquisition functions. First the existing MF modeling methods and MFO strategies are categorized to locate MF BO in a large family of surrogate-based optimization and MFO algorithms. Then, the common properties shared between the methods from each ingredient of MF BO are exploited to describe important GP-based MF surrogate models and to review various acquisition functions. This presentation aims to provide a structured understanding of MF BO. Finally, important aspects are examined 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 multiobjective optimization.