  We study active learning (AL) based on Gaussian Processes (GPs) for
efficiently enumerating all of the local minimum solutions of a black-box
function. This problem is challenging due to the fact that local solutions are
characterized by their zero gradient and positive-definite Hessian properties,
but those derivatives cannot be directly observed. We propose a new AL method
in which the input points are sequentially selected such that the confidence
intervals of the GP derivatives are effectively updated for enumerating local
minimum solutions. We theoretically analyze the proposed method and demonstrate
its usefulness through numerical experiments.
