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优雅的方法。然而，采集准则自身需要复杂的内部优化，这可能导致显著的计算开销。许多实用贝叶斯优化方法（尤其是在高维场景中）放弃了对采集函数进行形式化的连续优化，转而通过离散方式在有限的空间填充候选点集中进行搜索。本文提出使用位于当前设计点集Voronoi图边界上的候选点，使其与两个或多个设计点保持等距。我们讨论了无需显式生成Voronoi图即可直接采样其边界的有效实现策略，从而适用于高维度大规模设计。基于高斯过程与期望改进准则的测试问题集实验表明，本文方法在不损失精度的前提下显著提升了多起点连续搜索的执行效率。