Constrained Bayesian Optimization: A Review

Abstract

Bayesian optimization is a sequential optimization method that is particularly well suited for problems with limited computational budgets involving expensive and non-convex black-box functions. Though it has been widely used to solve various optimization tasks, most of the literature has focused on unconstrained settings, while many real-world problems are characterized by constraints. This paper reviews the current literature on single-objective constrained Bayesian optimization, classifying it according to three main algorithmic aspects: (i) the metamodel, (ii) the acquisition function, and (iii) the identification procedure. We discuss the current methods in each of these categories and conclude by a discussion of real-world applications and highlighting the main shortcomings in the literature, providing some promising directions for future research.

Keywords

• Bayesian optimization
• constrained optimization
• expensive black-box functions
• Gaussian processes