A Generalization of the Borkar-Meyn Theorem for Stochastic Recursive Inclusions

Ramaswamy, Arunselvan and Bhatnagar, Shalabh (2017) A Generalization of the Borkar-Meyn Theorem for Stochastic Recursive Inclusions. In: MATHEMATICS OF OPERATIONS RESEARCH, 42 (3). pp. 648-661.

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Abstract

In this paper, the stability theorem of Borkar and Meyn is extended to include the case when the mean field is a set-valued map. Two different sets of sufficient conditions are presented that guarantee the ``stability and convergence'' of stochastic recursive inclusions. Our work builds on the works of Benaim, Hofbauer and Sorin as well as Borkar and Meyn. As a corollary to one of the main theorems, a natural generalization of the Borkar and Meyn theorem follows. In addition, the original theorem of Borkar and Meyn is shown to hold under slightly relaxed assumptions. As an application to one of the main theorems, we discuss a solution to the ``approximate drift problem.'' Finally, we analyze the stochastic gradient algorithm with ``constant-error gradient estimators'' as yet another application of our main result.

Item Type:	Journal Article
Publication:	MATHEMATICS OF OPERATIONS RESEARCH
Additional Information:	Copy right for this article belongs to the INFORMS, 5521 RESEARCH PARK DR, SUITE 200, CATONSVILLE, MD 21228 USA
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	01 Sep 2017 09:20
Last Modified:	01 Sep 2017 09:20
URI:	http://eprints.iisc.ac.in/id/eprint/57714

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