Bayesian optimization (BO) is an efficient framework for solving black-box optimization problems with expensive function evaluations. This paper addresses the BO problem setting for combinatorial spaces (e.g., sequences and graphs) that occurs naturally in science and engineering applications. A prototypical example is molecular optimization guided by expensive experiments. The key challenge is to balance the complexity of statistical models and tractability of search to select combinatorial structures for evaluation. In this paper, we propose an efficient approach referred as Mercer Features for Combinatorial Bayesian Optimization (MerCBO). The key idea behind MerCBO is to provide explicit feature maps for diffusion kernels over discrete objects by exploiting the structure of their combinatorial graph representation. These Mercer features combined with Thompson sampling as the acquisition function allows us to employ tractable solvers to find next structures for evaluation. Experiments on diverse real-world benchmarks demonstrate that MerCBO performs similarly or better than prior methods. The source code is available at https://github.com/aryandeshwal/MerCBO .

本文介绍了Mercer Features for Combinatorial Bayesian Optimization（MerCBO）方法，该方法利用离散对象的组合图表示的结构，提供了扩散核的显式特征映射，结合使用Thompson采样作为获取函数，使我们能够使用可处理的解算器找到下一个要评估的结构，在各种真实世界基准测试中，MerCBO表现出类似或更好的结果。

高效组合贝叶斯优化的Mercer特征