Inexact proximal stochastic gradient method for convex composite optimization

doi:10.1007/s10589-017-9932-7

	Inexact proximal stochastic gradient method for convex composite optimization
	Wang, Xiao 1; Wang, Shuxiong 2; Zhang, Hongchao 3
刊名	COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
	2017-12-01
卷号	68 期号:3 页码:579-618
关键词	Convex composite optimization Empirical risk minimization Stochastic gradient Inexact methods Global convergence Complexity bound
ISSN号	0926-6003
DOI	10.1007/s10589-017-9932-7
英文摘要	We study an inexact proximal stochastic gradient (IPSG) method for convex composite optimization, whose objective function is a summation of an average of a large number of smooth convex functions and a convex, but possibly nonsmooth, function. Variance reduction techniques are incorporated in the method to reduce the stochastic gradient variance. The main feature of this IPSG algorithm is to allow solving the proximal subproblems inexactly while still keeping the global convergence with desirable complexity bounds. Different subproblem stopping criteria are proposed. Global convergence and the component gradient complexity bounds are derived for the both cases when the objective function is strongly convex or just generally convex. Preliminary numerical experiment shows the overall efficiency of the IPSG algorithm.
资助项目	National Natural Science Foundation of China[11301505] ; National Science Foundation of USA[1522654]
WOS研究方向	Operations Research & Management Science ; Mathematics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000415213800005
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/26874]
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Xiao
作者单位	1.Univ Chinese Acad Sci, Sch Math Sci, 19A Yuquan Rd, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Louisiana State Univ, Dept Math, 220 Lockett Hall, Baton Rouge, LA 70803 USA
推荐引用方式 GB/T 7714	Wang, Xiao,Wang, Shuxiong,Zhang, Hongchao. Inexact proximal stochastic gradient method for convex composite optimization[J]. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,2017,68(3):579-618.
APA	Wang, Xiao,Wang, Shuxiong,&Zhang, Hongchao.(2017).Inexact proximal stochastic gradient method for convex composite optimization.COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,68(3),579-618.
MLA	Wang, Xiao,et al."Inexact proximal stochastic gradient method for convex composite optimization".COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 68.3(2017):579-618.