A Domain-Shrinking based Bayesian Optimization Algorithm with Order-Optimal Regret Performance

Part of Advances in Neural Information Processing Systems 34 (NeurIPS 2021)

Authors

Sudeep Salgia, Sattar Vakili, Qing Zhao

Abstract

We consider sequential optimization of an unknown function in a reproducing kernel Hilbert space. We propose a Gaussian process-based algorithm and establish its order-optimal regret performance (up to a poly-logarithmic factor). This is the first GP-based algorithm with an order-optimal regret guarantee. The proposed algorithm is rooted in the methodology of domain shrinking realized through a sequence of tree-based region pruning and refining to concentrate queries in increasingly smaller high-performing regions of the function domain. The search for high-performing regions is localized and guided by an iterative estimation of the optimal function value to ensure both learning efficiency and computational efficiency. Compared with the prevailing GP-UCB family of algorithms, the proposed algorithm reduces computational complexity by a factor of $O(T^{2d-1})$ (where $T$ is the time horizon and $d$ the dimension of the function domain).