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SGD with momentum (SGDM) has been widely applied in many machine learning tasks, and it is often applied with dynamic stepsizes and momentum weights tuned in a stagewise manner. Despite of its empirical advantage over SGD, the role of momentum is still unclear in general since previous analyses on SGDM either provide worse convergence bounds than those of SGD, or assume Lipschitz or quadratic objectives, which fail to hold in practice. Furthermore, the role of dynamic parameters has not been addressed. In this work, we show that SGDM converges as fast as SGD for smooth objectives under both strongly convex and nonconvex settings. We also prove that multistage strategy is beneficial for SGDM compared to using fixed parameters. Finally, we verify these theoretical claims by numerical experiments.
Author Information
Yanli Liu (UCLA)
Yuan Gao (Columbia University)
I am a PhD student in Operations Research (IEOR) at Columbia University working on large-scale optimization in machine learning and decision-under-uncertainty. I have also passed the CFA Level I Exam.
Wotao Yin (Alibaba US, DAMO Academy)
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