Bayesian optimization (BO) offers an elegant approach for efficiently optimizing black-box functions. However, acquisition criteria demand their own challenging inner-optimization, which can induce significant overhead. Many practical BO methods, particularly in high dimension, eschew a formal, continuous optimization of the acquisition function and instead search discretely over a finite set of space-filling candidates. Here, we propose to use candidates which lie on the boundary of the Voronoi tessellation of the current design points, so they are equidistant to two or more of them. We discuss strategies for efficient implementation by directly sampling the Voronoi boundary without explicitly generating the tessellation, thus accommodating large designs in high dimension. On a battery of test problems optimized via Gaussian processes with expected improvement, our proposed approach significantly improves the execution time of a multi-start continuous search without a loss in accuracy.

翻译：贝叶斯优化（BO）为高效优化黑箱函数提供了一种优雅方法。然而，采集准则本身需要进行具有挑战性的内部优化，这可能带来显著的计算开销。许多实用的BO方法（尤其是在高维情况下）避免对采集函数进行形式化的连续优化，转而在一组有限的、具有空间填充特性的候选点上进行离散搜索。本文提出使用位于当前设计点的Voronoi镶嵌边界上的候选点，使其与两个或多个设计点保持等距。我们讨论了通过直接采样Voronoi边界而非显式生成镶嵌的高效实现策略，从而适应高维大规模设计。在通过高斯过程与期望改进进行优化的一系列测试问题上，我们提出的方法显著提升了多起点连续搜索的执行效率，且未损失精度。