Machine learning system, machine learning method, and program

Abstract

Machine learning techniques which allow machine learning to be performed even when a cost function is not a convex function are provided. A machine learning system includes a plurality of node portions which learn mapping that uses one common primal variable by machine learning based on their respective input data while sending and receiving information to and from each other. The machine learning is performed so as to minimize, instead of a cost function of a non-convex function originally corresponding to the machine learning, a proxy convex function serving as an upper bound on the cost function. The proxy convex function is represented by a formula of a first-order gradient of the cost function with respect to the primal variable or by a formula of a first-order gradient and a formula of a second-order gradient of the cost function with respect to the primal variable.