Yaji, VG and Bhatnagar, S (2020) Analysis of Stochastic Approximation Schemes with Set-Valued Maps in the Absence of a Stability Guarantee and Their Stabilization. In: IEEE Transactions on Automatic Control, 65 (3). pp. 1100-1115.
|
PDF
iee_tra_aut_con_65-3_1100-1115_2020.pdf - Published Version Download (522kB) | Preview |
Abstract
In this paper, we analyze the behavior of stochastic approximation schemes with set-valued maps in the absence of a stability guarantee. We prove that after a large number of iterations, if the stochastic approximation process enters the domain of attraction of an attracting set, it gets locked into the attracting set with high probability. We demonstrate that the above-mentioned result is an effective instrument for analyzing stochastic approximation schemes in the absence of a stability guarantee, by using it to obtain an alternate criterion for convergence in the presence of a locally attracting set for the mean field and by using it to show that a feedback mechanism, which involves resetting the iterates at regular time intervals, stabilizes the scheme when the mean field possesses a globally attracting set, thereby guaranteeing convergence. The results in this paper build on the works of Borkar, Andrieu et al., and Chen et al., by allowing for the presence of set-valued drift functions. © 1963-2012 IEEE.
| Item Type: | Journal Article |
|---|---|
| Publication: | IEEE Transactions on Automatic Control |
| Publisher: | Institute of Electrical and Electronics Engineers Inc. |
| Additional Information: | Copyright of this article belongs to Institute of Electrical and Electronics Engineers Inc. |
| Keywords: | Approximation theory; Set theory; Stabilization, Differential inclusions; Domain of attraction; Feedback mechanisms; High probability; Lock-in probability; Number of iterations; Set-valued map; Stochastic approximations, Stochastic systems |
| Department/Centre: | Division of Electrical Sciences > Computer Science & Automation |
| Date Deposited: | 21 Apr 2021 07:24 |
| Last Modified: | 21 Apr 2021 07:24 |
| URI: | http://eprints.iisc.ac.in/id/eprint/64958 |
Actions (login required)
 |
View Item |
