KMS Of Academy of mathematics and systems sciences, CAS
| Almost sure convergence of randomised-difference descent algorithm for stochastic convex optimisation | |
| Geng, Xiaoxue1,2; Huang, Gao3; Zhao, Wenxiao1,2 | |
| 2021-08-15 | |
| Source Publication | IET CONTROL THEORY AND APPLICATIONS
 |
| ISSN | 1751-8644 |
| Pages | 12 |
| Abstract | 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 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 Research Area | Automation & Control Systems ; Engineering ; Instruments & Instrumentation |
| WOS Subject | Automation & Control Systems ; Engineering, Electrical & Electronic ; Instruments & Instrumentation |
| WOS ID | WOS:000684957300001 |
| Publisher | WILEY |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/59105 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Zhao, Wenxiao |
| Affiliation | 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 |
| Recommended Citation 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. |
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