Surrogating the surrogate: accelerating Gaussian-process-based global optimization with a mixture cross-entropy algorithm

Rémi Bardenet, Balázs Kégl

Abstract: In global optimization, when the evaluation of the target function is costly, the usual strategy is to learn a surrogate model for the target function and replace the initial optimization by the optimization of the model. Gaussian processes have been widely used since they provide an elegant way to model the fitness and to deal with the exploration-exploitation trade-off in a principled way. Several empirical criteria have been proposed to drive the model optimization, among which is the well-known Expected Improvement criterion. The major computational bottleneck of these algorithms is the exhaustive grid search used to optimize the highly multimodal merit function. In this paper, we propose a competitive "adaptive grid" approach, based on a properly derived cross-entropy optimization algorithm with mixture proposals. Experiments suggest that 1) we outperform the classical single-Gaussian cross-entropy method when the fitness function is highly multimodal, and 2) we improve on standard exhaustive search in GP-based surrogate optimization.