Bayesian Optimization with Informative Covariance

Bayesian Optimization is a methodology for global optimization of unknown and expensive objectives. It combines a surrogate Bayesian regression model with an acquisition function to decide where to evaluate the objective. Typical regression models are Gaussian processes with stationary covariance functions, which, however, are unable to express prior input-dependent information, in particular information about possible locations of the optimum. The ubiquity of stationary models has led to the common practice of exploiting prior information via informative mean functions. In this paper, we highlight that these models can lead to poor performance, especially in high dimensions. We propose novel informative covariance functions that leverage nonstationarity to encode preferences for certain regions of the search space and adaptively promote local exploration during the optimization. We demonstrate that they can increase the sample efficiency of the optimization in high dimensions, even under weak prior information.