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Optimal distributed stochastic mirror descent for strongly convex optimization
Yuan, Deming1,2; Hong, Yiguang3; Ho, Daniel W. C.4; Jiang, Guoping2
2018-04-01
Source PublicationAUTOMATICA
ISSN0005-1098
Volume90Pages:196-203
AbstractIn this paper we consider convergence rate problems for stochastic strongly-convex optimization in the non-Euclidean sense with a constraint set over a time-varying multi-agent network. We propose two efficient non-Euclidean stochastic subgradient descent algorithms based on the Bregman divergence as distance-measuring function rather than the Euclidean distances that were employed by the standard distributed stochastic projected subgradient algorithms. For distributed optimization of non-smooth and strongly convex functions whose only stochastic subgradients are available, the first algorithm recovers the best previous known rate of O(ln(T)/T) (where T is the total number of iterations). The second algorithm is an epoch variant of the first algorithm that attains the optimal convergence rate of O(1/T), matching that of the best previously known centralized stochastic subgradient algorithm. Finally, we report some simulation results to illustrate the proposed algorithms. (C) 2018 Elsevier Ltd. All rights reserved.
KeywordDistributed stochastic optimization Strong convexity Non-Euclidean divergence Mirror descent Epoch gradient descent Optimal convergence rate
DOI10.1016/j.automatica.2017.12.053
Language英语
Funding ProjectNatural Science Fund for Excellent Young Scholars of Jiangsu Province[BK20170099] ; National Natural Science Foundation of China[61573344] ; National Natural Science Foundation of China[61733018] ; National Natural Science Foundation of China[61374180] ; Research Grants Council of the Hong Kong Special Administrative Region, China[CityU 11300415]
WOS Research AreaAutomation & Control Systems ; Engineering
WOS SubjectAutomation & Control Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000427217600022
PublisherPERGAMON-ELSEVIER SCIENCE LTD
Citation statistics
Cited Times:9[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29756
Collection系统科学研究所
Affiliation1.Nanjing Univ Sci & Technol, Sch Automat, Nanjing 210094, Jiangsu, Peoples R China
2.Nanjing Univ Posts & Telecommun, Coll Automat, Nanjing 210023, Jiangsu, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China
4.City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China
Recommended Citation
GB/T 7714
Yuan, Deming,Hong, Yiguang,Ho, Daniel W. C.,et al. Optimal distributed stochastic mirror descent for strongly convex optimization[J]. AUTOMATICA,2018,90:196-203.
APA Yuan, Deming,Hong, Yiguang,Ho, Daniel W. C.,&Jiang, Guoping.(2018).Optimal distributed stochastic mirror descent for strongly convex optimization.AUTOMATICA,90,196-203.
MLA Yuan, Deming,et al."Optimal distributed stochastic mirror descent for strongly convex optimization".AUTOMATICA 90(2018):196-203.
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