Global Convergence of Block Coordinate Descent in Deep Learning

TL;DR

This paper provides a theoretical framework demonstrating the global convergence of block coordinate descent methods in deep learning, including ResNets, with convergence rates established for common training models.

Contribution

It introduces a general methodology with convergence guarantees for BCD methods in deep neural network training, extending to various loss functions and architectures.

Findings

Proves global convergence of BCD in deep learning models.

Establishes a convergence rate of O(1/k).

Extends results to residual networks and general loss functions.

Abstract

Deep learning has aroused extensive attention due to its great empirical success. The efficiency of the block coordinate descent (BCD) methods has been recently demonstrated in deep neural network (DNN) training. However, theoretical studies on their convergence properties are limited due to the highly nonconvex nature of DNN training. In this paper, we aim at providing a general methodology for provable convergence guarantees for this type of methods. In particular, for most of the commonly used DNN training models involving both two- and three-splitting schemes, we establish the global convergence to a critical point at a rate of ${\cal O}(1/k)$, where $k$ is the number of iterations. The results extend to general loss functions which have Lipschitz continuous gradients and deep residual networks (ResNets). Our key development adds several new elements to the Kurdyka-{\L}ojasiewicz inequality framework that enables us to carry out the global convergence analysis of BCD in the general scenario of deep learning.