SGD Converges to Global Minimum in Deep Learning via Star-convex Path
Abstract
Stochastic gradient descent (SGD) has been found to be surprisingly effective in training a variety of deep neural networks. However, there is still a lack of understanding on how and why SGD can train these complex networks towards a global minimum. In this study, we establish the convergence of SGD to a global minimum for nonconvex optimization problems that are commonly encountered in neural network training. Our argument exploits the following two important properties: 1) the training loss can achieve zero value (approximately), which has been widely observed in deep learning; 2) SGD follows a star-convex path, which is verified by various experiments in this paper. In such a context, our analysis shows that SGD, although has long been considered as a randomized algorithm, converges in an intrinsically deterministic manner to a global minimum.
Cite
@article{arxiv.1901.00451,
title = {SGD Converges to Global Minimum in Deep Learning via Star-convex Path},
author = {Yi Zhou and Junjie Yang and Huishuai Zhang and Yingbin Liang and Vahid Tarokh},
journal= {arXiv preprint arXiv:1901.00451},
year = {2019}
}
Comments
ICLR2019