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arXiv · 1901.00451

SGD Converges to Global Minimum in Deep Learning via Star-convex Path

Yi Zhou·Junjie Yang·Huishuai Zhang·Yingbin Liang·Vahid Tarokh
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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.

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Yi Zhou, Junjie Yang, Huishuai Zhang, Yingbin Liang, Vahid Tarokh. 2019-01-02. SGD Converges to Global Minimum in Deep Learning via Star-convex Path. https://arxiv.org/abs/1901.00451

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