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

• URL: http://arxiv.org/abs/2010.13997v3
• Date: Fri, 29 Oct 2021 15:42:08 GMT
• Title: A Domain-Shrinking based Bayesian Optimization Algorithm with Order-Optimal Regret Performance
• Authors: Sudeep Salgia, Sattar Vakili, Qing Zhao
• Abstract summary: This is the first GP-based algorithm with an order-optimal regret guarantee. Compared with the prevailing GP-UCB family of algorithms, the proposed algorithm reduces computational complexity by a factor of $O(T2d-1)$.
• Score: 16.0251555430107
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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