Continuous simulation optimization with model mismatch using Gaussian process regression

Multi-fidelity simulation optimization is an emerging area looking at the use of low-fidelity (computationally cheap but inaccurate) models to optimize high-fidelity (expensive and accurate) models. In this context, low-fidelity models exhibit a mismatch to high-fidelity models whose values can be point-wise obtained by querying an expensive simulator. Herein, an efficient multi-fidelity algorithm is proposed for continuous global optimization. The algorithm is made up of an additive model that consolidates low-fidelity and bias (mismatch) predictions. Two sampling criteria with different use of the cumulated high and low-fidelity information are introduced as well as a cheap certificate guiding the decision on whether to sample from the expensive simulator. The performance of proposed algorithms is evaluated using a state of the art stochastic search benchmark algorithm. The results show that the proposed methods can beat the benchmark with improved accuracy, while essentially maintaining the same performance in terms of number of expensive simulations.