One-parameter family of acquisition functions for efficient global optimization

In diverse fields of science and engineering, one frequently faces the need to know the optimum of a black-box function that is expensive to evaluate. In materials science, in order to determine an optimal composition of alloys one has to repeat manual experiments that cost time and money. In machine learning model building, one has to tune a number of hyperparameters of a model but testing the performance of a model on big data via cross validation takes hours or even days. Thus, a framework is needed that provides a systematic means to minimize the number of queries needed to reach the optimal solution. Bayesian optimization (BO) [1-3] is a powerful methodology to seek an optimum of a black-box function without knowledge of its analytical properties, such as its gradient.