Active learning for enumerating local minima based on Gaussian process derivatives

When the evaluation of a blackbox function is expensive, it is often difficult to exhaustively investigate the function in the entire input domain. Active learning (AL) has been developed as a method for effectively selecting the input points at which the function evaluations are helpful for the target task. For example, if the target task is to find the global minimum, it is reasonable to evaluate the function at the input points which are likely to be global minima (this AL problem has been intensively studied in the context of Bayesian Optimization (BO) [9, 2, 1, 6, 14, 5]). In this paper, we study the problem of enumerating local minima (or maxima) of a black-box function. In many applications, it is beneficial to identify the positions of local minima and/or maxima because it helps to roughly grasp the "shape" of the black-box function.