Mercer Features for Efficient Combinatorial Bayesian Optimization

TL;DR

This paper introduces MerCBO, a novel method for combinatorial Bayesian optimization that uses explicit Mercer feature maps for diffusion kernels, enabling efficient search in complex discrete spaces like molecules.

Contribution

The paper proposes Mercer features for diffusion kernels in combinatorial BO, improving tractability and performance over prior methods.

Findings

MerCBO performs comparably or better than existing methods on real-world benchmarks.

Explicit Mercer features enable efficient optimization in combinatorial spaces.

The approach is applicable to diverse discrete structures such as sequences and graphs.

Abstract

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 .