论文标题
基于域的贝叶斯优化算法，具有订单最佳的遗憾性能
A Domain-Shrinking based Bayesian Optimization Algorithm with Order-Optimal Regret Performance
论文作者
论文摘要
我们考虑在繁殖的Hilbert空间中对未知函数的顺序优化。我们提出了一种基于高斯过程的算法，并建立了其秩序最佳的遗憾性能（直至多形因素）。这是第一个基于GP的算法，具有最佳的遗憾保证。所提出的算法植根于通过一系列基于树的区域修剪和精炼以在越来越小的功能域高绩效区域中浓缩查询的结构的方法。对高性能区域的搜索是由对最佳功能值的迭代估算进行局部和指导的，以确保学习效率和计算效率。与流行的GP-UCB算法家族相比，提出的算法将计算复杂性降低了$ O（t^{2d-1}）$（其中$ t $是时间范围，而$ d $ $ d $函数域的尺寸）。
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).
