UCSC-SOE-20-02: Bayesian Optimization via Barrier Functions

Tony Pourmohamad and Herbert K.H. Lee
05/03/2020 10:59 AM
Hybrid optimization methods that combine statistical modeling with mathematical programming have become a popular solution for Bayesian optimization 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 paper, we propose a novel Bayesian optimization strategy that combines response surface modeling with barrier methods to efficiently solve expensive constrained optimization problems in computer modeling. At the heart of all Bayesian optimization algorithms is an acquisition function for eff ectively 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 ensuring 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.