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SGD Converges to Global Minimum in Deep Learning via Star-convex Path
- Publication Year :
- 2019
- Publisher :
- arXiv, 2019.
-
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.<br />Comment: ICLR2019
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....9f1f0d9278c6fe6c7e944dddcbe1c292
- Full Text :
- https://doi.org/10.48550/arxiv.1901.00451