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Bayesian Optimization has become the reference method for the globaloptimization of black box, expensive and possibly noisy functions. BayesianOp-timization learns a probabilistic model about the objective function,usually a Gaussian Process, and builds, depending on its mean and variance, anacquisition function whose optimizer yields the new evaluation point, leadingto update the probabilistic surrogate model. Despite its sample efficiency,Bayesian Optimiza-tion does not scale well with the dimensions of the problem.The optimization of the acquisition function has received less attentionbecause its computational cost is usually considered negligible compared tothat of the evaluation of the objec-tive function. Its efficient optimizationis often inhibited, particularly in high di-mensional problems, by multipleextrema. In this paper we leverage the addition-ality of the objective functioninto mapping both the kernel and the acquisition function of the BayesianOptimization in lower dimensional subspaces. This ap-proach makes moreefficient the learning/updating of the probabilistic surrogate model and allowsan efficient optimization of the acquisition function. Experi-mental resultsare presented for real-life application, that is the control of pumps in urbanwater distribution systems.

Composition of kernel and acquisition functions for High Dimensional Bayesian Optimization