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

21 May 2021, 20:47 (edited 26 Oct 2021)NeurIPS 2021 PosterReaders: Everyone
• Keywords: Gaussian Process Bandit, Bayesian Optimization, Kernelized Model, RKHS, Optimal Regret Bounds
• 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).
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