Advancing Gaussian Process Bandit Optimization for Time-Varying Functions

Abstract

This thesis investigates the problem of time-varying function optimization. In particular, we study techniques to minimize the cumulative regret when optimizing a time-varying function in the Gaussian process setting. First, we introduce the problem and present a literature review of the current methods and results. Following this, we we propose enhancements to existing algorithms, demonstrating improved regret bounds. We discuss the applications of these algorithms and where they can provide a benefit compared to existing methods. With these applications in mind we introduce two new temporal models for time-varying functions and their associated algorithms. We test their performance in order to validate their effectiveness and potential benefits.