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

doi:10.1049/cth2.12184

CSpace

	Almost sure convergence of randomised-difference descent algorithm for stochastic convex optimisation
	Geng, Xiaoxue 1,2; Huang, Gao 3; Zhao, Wenxiao 1,2
	2021-08-15
发表期刊	IET CONTROL THEORY AND APPLICATIONS
ISSN	1751-8644
页码	12
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.
DOI	10.1049/cth2.12184
收录类别	SCI
语种	英语
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
WOS类目	Automation & Control Systems ; Engineering, Electrical & Electronic ; Instruments & Instrumentation
WOS记录号	WOS:000684957300001
出版者	WILEY
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59105
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.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Tsinghua Univ, Dept Automat, Beijing, 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.