A Bi-Objective Optimization Based Acquisition Strategy for Batch Bayesian Global Optimization

In this paper we deal with batch Bayesian Optimization (Bayes-Opt) problems over a box. Bayes-Opt approaches find their main applications when the objective function is very expensive to evaluate. Sometimes, given the availability of multi-processor computing architectures, function evaluation might be performed in parallel in order to lower the clock-time of the overall computation. This paper fits this situation and is devoted to the development of a novel bi-objective optimization (BOO) acquisition strategy to sample batches of points where to evaluate the objective function. The BOO problem involves the Gaussian Process posterior mean and variance functions, which, in most of the acquisition strategies from the literature, are generally used in combination, frequently through scalarization. However, such scalarization could compromise the Bayes-Opt process performance, as getting the desired trade-off between exploration and exploitation is not trivial in most cases. We instead aim to reconstruct the Pareto front of the BOO problem exploiting first order information of the posterior mean and variance, thus generating multiple trade-offs of the two functions without any a priori knowledge. The algorithm used for the reconstruction is the Non-dominated Sorting Memetic Algorithm (NSMA), recently proposed in the literature and proved to be effective in solving hard MOO problems. Finally, we present two clustering approaches, each of them operating on a different space, to select potentially optimal points from the Pareto front. We compare our methodology with well-known acquisition strategies from the literature, showing its effectiveness on a wide set of experiments.