Keywords: surrogate modeling, Gaussian process, active learning, sequential design, space-filling design, Delaunay triangulation, convex hull
TL;DR: We propose candidates for Bayesian optimization of a black box function using Delaunay triangulation of existing training data locations.
Abstract: Bayesian optimization involves "inner optimization" over a new-data acquisition criterion which is non-convex/highly multi-modal, may be non-differentiable, or may otherwise thwart local numerical optimizers. In such cases it is common to replace continuous search with a discrete one over random candidates. Here we propose using candidates based on a Delaunay triangulation of the existing input design. We detail the construction of these "tricands" and demonstrate empirically how they outperform both numerically optimized acquisitions and random candidate-based alternatives, and are well-suited for hybrid schemes, on benchmark synthetic and real simulation experiments.
Supplementary Material: pdf