Surrogate-based Optimization using Mutual Information for Computer Experiments (optim-MICE)

Abstract: The computational burden of running a complex computer model can make optimization impractical. Gaussian Processes (GPs) are statistical surrogates (also known as emulators) that alleviate this issue since they cheaply replace the computer model. As a result, the exploration vs. exploitation trade-off strategy can be accelerated by building a GP surrogate. In this paper, we propose a new surrogate-based optimization scheme that minimizes the number of evaluations of the computationally expensive function. Taking advantage of parallelism of the evaluation of the unknown function, the uncertain regions are explored simultaneously, and a batch of input points is chosen using Mutual Information for Computer Experiments (MICE), a sequential design algorithm which maximizes the information theoretic Mutual Information over the input space. The computational efficiency of interweaving the optimization scheme with MICE (optim-MICE) is examined and demonstrated on test functions. Optim-MICE is compared with state-of-the-art heuristics such as Efficient Global Optimization (EGO) and GP-Upper Confidence Bound (GP-UCB). We demonstrate that optim-MICE outperforms these schemes on a large range of computational experiments.