Adaptive Replication Strategies in Trust-Region-Based Bayesian Optimization of Stochastic Functions

We develop and analyze a method for stochastic simulation optimization relying on Gaussian process models within a trust-region framework. We are interested in the case when the variance of the objective function is large. We propose to rely on replication and local modeling to cope with this high-throughput regime, where the number of evaluations may become large to get accurate results while still keeping good performance. We propose several schemes to encourage replication, from the choice of the acquisition function to setup evaluation costs. Compared with existing methods, our results indicate good scaling, in terms of both accuracy (several orders of magnitude better than existing methods) and speed (taking into account evaluation costs).