Bayesian optimization is a sample-efficient method for finding a global optimum of an expensive-to-evaluate black-box function. A global solution is found by accumulating a pair of query point and corresponding function value, repeating these two procedures: (i) learning a surrogate model for the objective function using the data observed so far; (ii) the maximization of an acquisition function to determine where next to query the objective function. Convergence guarantees are only valid when the global optimizer of the acquisition function is found and selected as the next query point. In practice, however, local optimizers of acquisition functions are also used, since searching the exact optimizer of the acquisition function is often a non-trivial or time-consuming task. In this paper we present an analysis on the behavior of local optimizers of acquisition functions, in terms of instantaneous regrets over global optimizers. We also present the performance analysis when multi-started local optimizers are used to find the maximum of the acquisition function. Numerical experiments confirm the validity of our theoretical analysis.

本文介绍了贝叶斯优化的方法，通过建模替代函数和最大化收购功能来确定下一步查询的位置，同时考虑三种流行的收购功能的局部优化器的性能分析，并引入允许本地优化方法从多个不同的起始条件开始的分析，数值实验证实了我们的理论分析的有效性。

贝叶斯优化的收购函数的本地优化器