Dynamic Random Feature Gaussian Processes for Bayesian Optimization of Time-Varying Functions

Bayesian optimization (BO) is a popular approach to optimizing costly, black-box functions that rely on a statistical surrogate model of the function to select new query points, balancing exploration and exploitation of the parameter space. Most of the work on BO has focused on the time-invariant setting where the function does not change over time. Recently, the time-varying BO (TV-BO) framework has been introduced to handle non-stationary functions. In this work, we explore TV-BO with the use of dynamic random feature-based Gaussian processes (DRF-GPs). These processes capture the nonstationarity of the unknown functions by evolving the parameter vector of a linear model. We propose an evolution mechanism that results in an acquisition function with sensible exploitation-exploration trade-offs over time. We compare the resulting algorithm with the TV-BO baseline algorithms on a toy example and a localization problem with synthetic data.