Title: Training By Vanilla SGD with Larger Learning Rates. Abstract: The stochastic gradient descent (SGD) method, first proposed in 1950's, has been the foundation for deep-neural-network (DNN) training with numerous enhancements including adding a momentum or adaptively selecting learning rates, or using both strategies and more.  A common view for SGD is that the learning rate should be eventually made small in order to reach sufficiently good approximate solutions.  Another widely held view is that the vanilla SGD is out of fashion in comparison to many of its modern variations.  In this work, we provide a contrarian claim that, when training over-parameterized DNNs, the vanilla SGD can still compete well with, and oftentimes outperform, its more recent variations by simply using learning rates significantly larger than commonly used values.  We establish theoretical results to explain this local convergence behavior of SGD on nonconvex functions, and also present computational evidence, across multiple tasks including image classification, speech recognition and natural language processing, to support the practice of using larger learning rates.
