Using Past Experience for Configuration of Gaussian Processes in Black-Box Optimization

Abstract

This paper deals with the configuration of Gaussian processes serving as surrogate models in black-box optimization. It examines several different covariance functions of Gaussian processes (GPs) and a combination of GPs and artificial neural networks (ANNs). Different configurations are compared in the context of a surrogate-assisted version of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), a state-of-the-art evolutionary black-box optimizer. The configuration employs a new methodology, which consists of using data from past runs of the optimizer. In that way, it is possible to avoid demanding computations of the optimizer only to configure the surrogate model as well as to achieve a much more robust configuration relying on 4600 optimization runs in 5 different dimensions. The experimental part reveals that the lowest rank difference error, an error measure corresponding to the CMA-ES invariance with respect to monotonous transformations, is most often achieved using rational quadratic, squared exponential and Matérn 5/2 kernels. It also reveals that these three covariance functions are always equivalent, in the sense that the differences between their errors are never statistically significant. In some cases, they are also equivalent to other configurations, including the combination ANN-GP.