Fig. 2: Overall pipeline for customized acquisition function design using Bayesian algorithm execution.

a Example of a user specified algorithm (Level Band) executed on a true and unknown measured property. Here, the target subset of the design space are the specific set of design points which have measured property values which fall within the specified level band. b An illustration of using a Gaussian Process model (\({{{\mathcal{GP}}}}\)) which predicts a mean value (red curve) and an uncertainty (blue band) for every point in the design space, and can fit measured data sampled from the true function. Posterior function samples (\({\{{f}_{i}\}}_{i = 1}^{n}\)) are obtained from this probabilistic model via sampling and represent statistically consistent guesses of the true function based on measured training data. c The user algorithm can be executed on either the posterior samples or the posterior mean to build the d BAX acquisition functions (InfoBAX and MeanBAX). The next suggested point to measure corresponds to the design point with the highest acquisition value.