Supplemental Materials Re Examining Linear for High Dimensional Bayesian Optimization

As explained in Sec. 4, with Within the first embedding, the optimal value of 0.398 can be reached. As described in Sec. 5, we show the importance of the Mahalanobis kernel using models fit to Fig. S2 compares model predictions for each of these models with the actual test-set outcomes; results Fig. S3 evaluates the predictive log marginal probabilities for the ARD RBF kernel and the Ma-halanobis kernel with posterior sampling across a wide range of training sets with different sizes Mahalanobis kernel is able to learn as the training set is expanded. This can be seen in the optimization results (Figs. 5 and S7) where ALEBO The implied kernel on the embedding is thus stationary. The argument follows that of Prop. 1. Linear embedding HDBO requires selecting a dimensionality for the embedding. The nature of the dimensionality vs. iteration budget trade-off is important in all These same considerations apply to multi-objective optimization.