SAdam: A Variant of Adam for Strongly Convex FunctionsDownload PDF

25 Sept 2019, 19:18 (modified: 11 Mar 2020, 07:34)ICLR 2020 Conference Blind SubmissionReaders: Everyone
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Keywords: Online convex optimization, Adaptive online learning, Adam
TL;DR: A variant of Adam for strongly convex functions
Abstract: The Adam algorithm has become extremely popular for large-scale machine learning. Under convexity condition, it has been proved to enjoy a data-dependent $O(\sqrt{T})$ regret bound where $T$ is the time horizon. However, whether strong convexity can be utilized to further improve the performance remains an open problem. In this paper, we give an affirmative answer by developing a variant of Adam (referred to as SAdam) which achieves a data-dependent $O(\log T)$ regret bound for strongly convex functions. The essential idea is to maintain a faster decaying yet under controlled step size for exploiting strong convexity. In addition, under a special configuration of hyperparameters, our SAdam reduces to SC-RMSprop, a recently proposed variant of RMSprop for strongly convex functions, for which we provide the first data-dependent logarithmic regret bound. Empirical results on optimizing strongly convex functions and training deep networks demonstrate the effectiveness of our method.
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