Bayesian Optimization Via Barrier Functions

Hybrid optimization methods that combine statistical modeling with mathematical programming have become a popular solution for Bayesian optimization (BO) because they can better leverage both the efficient local search properties of the numerical method and the global search properties of the statistical model. These methods seek to create a sequential design strategy for efficiently optimizing expensive black-box functions when gradient information is not readily available. In this article, we propose a novel BO strategy that combines response surface modeling with barrier methods to efficiently solve expensive constrained optimization problems in computer modeling. At the heart of all BO algorithms is an acquisition function for effectively guiding the search. Our hybrid algorithm is guided by a novel acquisition function that tries to decrease the objective function as much as possible while simultaneously trying to ensure that the boundary of the constraint space is never crossed. Illustrations highlighting the success of our method are provided, including a real-world computer model optimization experiment from hydrology. Supplementary files for this article are available online.