Title
SAdam: 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.
Year
Venue
Keywords
2019
arXiv: Learning
Online convex optimization, Adaptive online learning, Adam
DocType
Volume
Citations 
Journal
abs/1905.02957
0
PageRank 
References 
Authors
0.34
0
5
Name
Order
Citations
PageRank
Guanghui Wang101.35
Lu, Shiyin203.38
Quan Cheng300.34
Wei-Wei Tu4337.86
Lijun Zhang598063.68