Information-theoretic acquisition functions. The principle behind acquisition functions based on information theory is to select the NPM x that maximizes the mutual information between (i) the observation of its property y =f (x) and (ii) the location of the NPM x * in feature space that maximizes f (x). Viewing both f (x) and x * as random variables, the following acquisition function describes the mutual information between the observation (x, y = f (x)) of the property of a newly acquired NPM, x, and the location of the optimal NPM, x * .