The Strength of Nesterov's Extrapolation in the Individual Convergence of Nonsmooth Optimization

doi:10.1109/TNNLS.2019.2933452

CASIA OpenIR > 多模态人工智能系统全国重点实验室 > 人工智能与机器学习（杨雪冰）-技术团队

	The Strength of Nesterov's Extrapolation in the Individual Convergence of Nonsmooth Optimization
	Tao, Wei 1; Pan, Zhisong 1; Wu, Gaowei2 ; Tao, Qing 2,3
发表期刊	IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
ISSN	2162-237X
	2020-07-01
卷号	31 期号:7 页码:2557-2568
通讯作者	Tao, Qing(taoqing@gmail.com)
摘要	The extrapolation strategy raised by Nesterov, which can accelerate the convergence rate of gradient descent methods by orders of magnitude when dealing with smooth convex objective, has led to tremendous success in training machine learning tasks. In this article, the convergence of individual iterates of projected subgradient (PSG) methods for nonsmooth convex optimization problems is theoretically studied based on Nesterov's extrapolation, which we name individual convergence. We prove that Nesterov's extrapolation has the strength to make the individual convergence of PSG optimal for nonsmooth problems. In light of this consideration, a direct modification of the subgradient evaluation suffices to achieve optimal individual convergence for strongly convex problems, which can be regarded as making an interesting step toward the open question about stochastic gradient descent (SGD) posed by Shamir. Furthermore, we give an extension of the derived algorithms to solve regularized learning tasks with nonsmooth losses in stochastic settings. Compared with other state-of-the-art nonsmooth methods, the derived algorithms can serve as an alternative to the basic SGD especially in coping with machine learning problems, where an individual output is needed to guarantee the regularization structure while keeping an optimal rate of convergence. Typically, our method is applicable as an efficient tool for solving large-scale l(1)-regularized hinge-loss learning problems. Several comparison experiments demonstrate that our individual output not only achieves an optimal convergence rate but also guarantees better sparsity than the averaged solution.
关键词	Convergence Extrapolation Optimization Acceleration Machine learning Task analysis Machine learning algorithms Individual convergence machine learning Nesterov's extrapolation nonsmooth optimization sparsity
DOI	10.1109/TNNLS.2019.2933452
收录类别	SCI
语种	英语
资助项目	NSFC[61673394] ; National Key Research and Development Program of China[2016QY03D0501]
项目资助者	NSFC ; National Key Research and Development Program of China
WOS研究方向	Computer Science ; Engineering
WOS类目	Computer Science, Artificial Intelligence ; Computer Science, Hardware & Architecture ; Computer Science, Theory & Methods ; Engineering, Electrical & Electronic
WOS记录号	WOS:000546986600027
出版者	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
引用统计	被引频次：10[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://ir.ia.ac.cn/handle/173211/40051
专题	多模态人工智能系统全国重点实验室_人工智能与机器学习（杨雪冰）-技术团队
通讯作者	Tao, Qing
作者单位	1.Army Engn Univ PLA, Command & Control Engn Coll, Nanjing 210007, Peoples R China 2.Chinese Acad Sci, Inst Automat, Beijing, Peoples R China 3.Army Acad Artillery & Air Def, Hefei 230031, Peoples R China
通讯作者单位	中国科学院自动化研究所
推荐引用方式 GB/T 7714	Tao, Wei,Pan, Zhisong,Wu, Gaowei,et al. The Strength of Nesterov's Extrapolation in the Individual Convergence of Nonsmooth Optimization[J]. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS,2020,31(7):2557-2568.
APA	Tao, Wei,Pan, Zhisong,Wu, Gaowei,&Tao, Qing.(2020).The Strength of Nesterov's Extrapolation in the Individual Convergence of Nonsmooth Optimization.IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS,31(7),2557-2568.
MLA	Tao, Wei,et al."The Strength of Nesterov's Extrapolation in the Individual Convergence of Nonsmooth Optimization".IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 31.7(2020):2557-2568.