Random Exploration in Bayesian Optimization: Order-Optimal Regret and Computational Efficiency
This work provides a more efficient and theoretically sound method for Bayesian optimization, which is incremental but addresses key bottlenecks in computational cost and regret guarantees for researchers and practitioners in machine learning.
The paper tackles the problem of efficiently exploring the domain in Bayesian optimization by using random sampling, showing that this approach achieves optimal error rates and resolves an open problem in regret performance for noise-free settings. It also demonstrates computational advantages over existing methods by avoiding expensive optimization steps.
We consider Bayesian optimization using Gaussian Process models, also referred to as kernel-based bandit optimization. We study the methodology of exploring the domain using random samples drawn from a distribution. We show that this random exploration approach achieves the optimal error rates. Our analysis is based on novel concentration bounds in an infinite dimensional Hilbert space established in this work, which may be of independent interest. We further develop an algorithm based on random exploration with domain shrinking and establish its order-optimal regret guarantees under both noise-free and noisy settings. In the noise-free setting, our analysis closes the existing gap in regret performance and thereby resolves a COLT open problem. The proposed algorithm also enjoys a computational advantage over prevailing methods due to the random exploration that obviates the expensive optimization of a non-convex acquisition function for choosing the query points at each iteration.