Here we summarize implementation details and experimental results that were removed from the main body of the paper due to space constraints. All of the empirical work in our paper is fully reproducible. Code may be found in our git repository: http://bitbucket.org/gramacylab/tricands . The GP surrogate for the Goldstein-Price and Hartman 6 examples (Section 3 and Appendix A.2, respectively) used the Gramacy [2020], modified to keep track of the number of evaluations. The heteroskedastic GP surrogate used for A TO (Section 3.2) was via Sometimes this resulted in replications in the design.

Bayesian optimization involves "inner optimization" over a new-data acquisition

Bayesian optimization is a form of sequential design: idealize input-output relationships with a suitably flexible nonlinear regression model; fit to data from an initial experimental campaign; devise and optimize a criterion for selecting the next experimental condition(s) under the fitted model (e.g., via predictive equations) to target outcomes of interest (say minima); repeat after acquiring output under those conditions and updating the fit. In many situations this "inner optimization" over the new-data acquisition criterion is cumbersome because it is non-convex/highly multi-modal, may be non-differentiable, or may otherwise thwart numerical optimizers, especially when inference requires Monte Carlo. In such cases it is not uncommon 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. In addition to detailing construction of these "tricands", based on a simple wrapper around a conventional convex hull library, we promote several advantages based on properties of the geometric criterion involved. We then demonstrate empirically how tricands can lead to better Bayesian optimization performance compared to both numerically optimized acquisitions and random candidate-based alternatives on benchmark problems.