Expected Regret Minimization for Bayesian Optimization with Student's-t Processes

Abstract

Student's-t Processes were recently proposed as a probabilistic alternative to Gaussian Processes for Bayesian optimization. Student's-t Processes are a generalization of Gaussian Processes, using an extra parameter v, which addresses Gaussian Processes' weaknesses. Separately, recent work used prior knowledge of a black-box function's global optimum f*, to create a new acquisition function for Bayesian optimization called Expected Regret Minimization. Gaussian Processes were then combined with Expected Regret Minimization to outperform existing models for Bayesian optimization. No published work currently exists for Expected Regret Minimization with Student's-t Processes. This research compares Expected Regret Minimization for Bayesian optimization, using Student's-t Processes versus Gaussian Processes. Both models are applied to four problems popular in mathematical optimization. Our work enhances Bayesian optimization by showing superior training regret minimization for Expected Regret Minimization, using Student's-t Processes versus Gaussian Processes.