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Almost sure convergence of randomised-difference descent algorithm for stochastic convex optimisation

文献类型：期刊论文

作者Geng, Xiaoxue2,3; Huang, Gao1; Zhao, Wenxiao2,3
刊名IET CONTROL THEORY AND APPLICATIONS
出版日期2021-08-15
页码12
ISSN号1751-8644
DOI10.1049/cth2.12184
英文摘要Stochastic gradient descent algorithm is a classical and useful method for stochastic optimisation. While stochastic gradient descent has been theoretically investigated for decades and successfully applied in machine learning such as training of deep neural networks, it essentially relies on obtaining the unbiased estimates of gradients/subgradients of the objective functions. In this paper, by constructing the randomised differences of the objective function, a gradient-free algorithm, named the stochastic randomised-difference descent algorithm, is proposed for stochastic convex optimisation. Under the strongly convex assumption of the objective function, it is proved that the estimates generated from stochastic randomised-difference descent converge to the optimal value with probability one, and the convergence rates of both the mean square error of estimates and the regret functions are established. Finally, some numerical examples are prsented.
资助项目National Key Research and Development Program of China[2018YFA0703800] ; National Nature Science Foundation of China[62022048] ; Strategic Priority Research Program of Chinese Academy of Sciences[XDA27000000]
WOS研究方向Automation & Control Systems ; Engineering ; Instruments & Instrumentation
语种英语
出版者WILEY
WOS记录号WOS:000684957300001
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/59104]  
专题中国科学院数学与系统科学研究院
通讯作者Zhao, Wenxiao
作者单位1.Tsinghua Univ, Dept Automat, Beijing, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China
推荐引用方式
GB/T 7714		 Geng, Xiaoxue,Huang, Gao,Zhao, Wenxiao. Almost sure convergence of randomised-difference descent algorithm for stochastic convex optimisation[J]. IET CONTROL THEORY AND APPLICATIONS,2021:12.
APA Geng, Xiaoxue,Huang, Gao,&Zhao, Wenxiao.(2021).Almost sure convergence of randomised-difference descent algorithm for stochastic convex optimisation.IET CONTROL THEORY AND APPLICATIONS,12.
MLA Geng, Xiaoxue,et al."Almost sure convergence of randomised-difference descent algorithm for stochastic convex optimisation".IET CONTROL THEORY AND APPLICATIONS (2021):12.

入库方式： OAI收割

来源：数学与系统科学研究院

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