Gradient-enhanced Kriging for high-dimensional Bayesian optimization with linear embedding

This paper explores the application of gradient-enhanced Kriging model for high-dimensional Bayesian optimization (BO) with linear embedding. We embed the original high-dimensional space in a low-dimensional subspace by analyzing the spectrum of the second-moment matrix of the gradient of the function response based on the active subspace method. By mapping the training data into their respective subspace, the objective function and the constraint functions are approximated with low-dimensional GE-Kriging models efficiently. In each cycle of the BO procedure, a new point is found by maximizing the constrained expected improvement function within a low-dimensional polytope, and it is mapped back to the original space for model evaluation. The experiment results show that the proposed method is promising for optimizing high-dimensional expensive problems, especially for problems that exhibit a clear low-dimensional active subspace.