Frank-Wolfe optimization for deep networks

TL;DR

This paper explores the application of Frank-Wolfe optimization to deep neural networks, comparing its convergence and stability to traditional gradient descent, and finds it converges slowly and is unstable in stochastic settings.

Contribution

It introduces the use of Frank-Wolfe optimization for training deep networks and evaluates its performance relative to gradient descent.

Findings

Frank-Wolfe converges slowly compared to gradient descent.

In stochastic settings, Frank-Wolfe is unstable without line search.

Gradient descent remains more effective for deep network training.

Abstract

Deep neural networks is today one of the most popular choices in classification, regression and function approximation. However, the training of such deep networks is far from trivial as there are often millions of parameters to tune. Typically, one use some optimization method that hopefully converges towards some minimum. The most popular and successful methods are based on gradient descent. In this paper, another optimization method, Frank-Wolfe optimization, is applied to a small deep network and compared to gradient descent. Although the optimization does converge, it does so slowly and not close to the speed of gradient descent. Further, in a stochastic setting, the optimization becomes very unstable and does not seem to converge unless one uses a line search approach.