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Robustness to Unbounded Smoothness of Generalized SignSGD
Michael Crawshaw · Mingrui Liu · Francesco Orabona · Wei Zhang · Zhenxun Zhuang

Wed Nov 30 02:00 PM -- 04:00 PM (PST) @ Hall J #413

Traditional analyses in non-convex optimization typically rely on the smoothness assumption, namely requiring the gradients to be Lipschitz. However, recent evidence shows that this smoothness condition does not capture the properties of some deep learning objective functions, including the ones involving Recurrent Neural Networks and LSTMs. Instead, they satisfy a much more relaxed condition, with potentially unbounded smoothness. Under this relaxed assumption, it has been theoretically and empirically shown that the gradient-clipped SGD has an advantage over the vanilla one. In this paper, we show that clipping is not indispensable for Adam-type algorithms in tackling such scenarios: we theoretically prove that a generalized SignSGD algorithm can obtain similar convergence rates as SGD with clipping but does not need explicit clipping at all. This family of algorithms on one end recovers SignSGD and on the other end closely resembles the popular Adam algorithm. Our analysis underlines the critical role that momentum plays in analyzing SignSGD-type and Adam-type algorithms: it not only reduces the effects of noise, thus removing the need for large mini-batch in previous analyses of SignSGD-type algorithms, but it also substantially reduces the effects of unbounded smoothness and gradient norms. To the best of our knowledge, this work is the first one showing the benefit of Adam-type algorithms compared with non-adaptive gradient algorithms such as gradient descent in the unbounded smoothness setting. We also compare these algorithms with popular optimizers on a set of deep learning tasks, observing that we can match the performance of Adam while beating others.

Author Information

Michael Crawshaw (George Mason University)
Mingrui Liu (George Mason University)
Francesco Orabona (Boston University)
Wei Zhang (IBM T.J.Watson Research Center)

BE Beijing Univ of Technology 2005 MSc Technical University of Denmark 2008 PhD University of Wisconsin, Madison 2013 All in computer science Published papers in ASPLOS, OOPSLA, OSDI, PLDI, IJCAI, ICDM, NIPS

Zhenxun Zhuang (Meta)

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