A Globally Convergent Algorithm for Neural Network Parameter Optimization Based on Difference-of-Convex Functions

TL;DR

An algorithm for optimizing the parameters of single hidden layer neural networks is proposed that is combined with a tailored difference-of-convex functions algorithm (DCA) and it is proved global convergence of the proposed algorithm.

Abstract

We propose an algorithm for optimizing the parameters of single hidden layer neural networks. Specifically, we derive a blockwise difference-of-convex (DC) functions representation of the objective function. Based on the latter, we propose a block coordinate descent (BCD) approach that we combine with a tailored difference-of-convex functions algorithm (DCA). We prove global convergence of the proposed algorithm. Furthermore, we mathematically analyze the convergence rate of parameters and the convergence rate in value (i.e., the training loss). We give conditions under which our algorithm converges linearly or even faster depending on the local shape of the loss function. We confirm our theoretical derivations numerically and compare our algorithm against state-of-the-art gradient-based solvers in terms of both training loss and test loss.