Stochastic In-Face Frank-Wolfe Methods for Non-Convex Optimization and Sparse Neural Network Training
This work addresses the challenge of efficiently training sparse neural networks, which is important for reducing model complexity and computational costs in machine learning applications, though it appears incremental as it builds upon existing Frank-Wolfe methods.
The authors tackled the problem of training sparse neural networks by introducing a new variant of the Frank-Wolfe method that combines Frank-Wolfe and steepest descent steps, with a modified gap for non-convex optimization, resulting in significant improvements in training sparse neural networks as demonstrated in numerical experiments on artificial and real datasets.
The Frank-Wolfe method and its extensions are well-suited for delivering solutions with desirable structural properties, such as sparsity or low-rank structure. We introduce a new variant of the Frank-Wolfe method that combines Frank-Wolfe steps and steepest descent steps, as well as a novel modification of the "Frank-Wolfe gap" to measure convergence in the non-convex case. We further extend this method to incorporate in-face directions for preserving structured solutions as well as block coordinate steps, and we demonstrate computational guarantees in terms of the modified Frank-Wolfe gap for all of these variants. We are particularly motivated by the application of this methodology to the training of neural networks with sparse properties, and we apply our block coordinate method to the problem of $\ell_1$ regularized neural network training. We present the results of several numerical experiments on both artificial and real datasets demonstrating significant improvements of our method in training sparse neural networks.