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Bayesian optimization is a popular method for solving the problem of globaloptimization of an expensive-to-evaluate black-box function. It relies on aprobabilistic surrogate model of the objective function, upon which anacquisition function is built to determine where next to evaluate the objectivefunction. In general, Bayesian optimization with Gaussian process regressionoperates on a continuous space. When input variables are categorical ordiscrete, an extra care is needed. A common approach is to use one-hot encodedor Boolean representation for categorical variables which might yield acombinatorial explosion problem. In this paper we present a method for Bayesianoptimization in a combinatorial space, which can operate well in a largecombinatorial space. The main idea is to use a random mapping which embeds thecombinatorial space into a convex polytope in a continuous space, on which allessential process is performed to determine a solution to the black-boxoptimization in the combinatorial space. We describe our combinatorial Bayesianoptimization algorithm and present its regret analysis. Numerical experimentsdemonstrate that our method shows satisfactory performance compared to existingmethods.

Combinatorial Bayesian Optimization with Random Mapping Functions to Convex Polytopes