Efficient spatial designs using Hausdorff distances and Bayesian optimization

An iterative Bayesian optimization technique is presented to find spatial designs of data that carry much information. We use the decision theoretic notion of value of information as the design criterion. Gaussian process surrogate models enable fast calculations of expected improvement for a large number of designs, while the full-scale value of information evaluations are only done for the most promising designs. The Hausdorff distance is used to model the similarity between designs in the surrogate Gaussian process covariance representation, and this allows the suggested algorithm to learn across different designs. We study properties of the Bayesian optimization design algorithm in a synthetic example and real-world examples from forest conservation and petroleum drilling operations. In the synthetic example we consider a model where the exact solution is available and we run the algorithm under different versions of this example and compare it with existing approaches such as sequential selection and an exchange algorithm