Bayesian Optimization of Unimodal Functions

Bayesian Optimization (BO) is a global optimization strategy designed to find the minimum of a black-box function by using a Gaussian process (GP) as a surrogate model for the function to be optimized. In this work, we study learning and optimization of unimodal functions using Bayesian optimization. We propose a hierarchical model for unimodal functions based on Gaussian processes with virtual derivative observations. We demonstrate that taking such structural prior information into account can decrease the number of function evaluations significantly and improve data efficiency.