Stochastic recursive inclusions with non-additive iterate-dependent Markov noise

Yaji, Vinayaka G. ; Bhatnagar, Shalabh (2018) Stochastic recursive inclusions with non-additive iterate-dependent Markov noise Stochastics, 90 (3). pp. 330-363. ISSN 1744-2508

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Official URL: http://doi.org/10.1080/17442508.2017.1353984

Related URL: http://dx.doi.org/10.1080/17442508.2017.1353984

Abstract

In this paper we study the asymptotic behaviour of stochastic approximation schemes with set-valued drift function and non-additive iterate-dependent Markov noise. We show that a linearly interpolated trajectory of such a recursion is an asymptotic pseudotrajectory for the flow of a limiting differential inclusion obtained by averaging the set-valued drift function of the recursion w.r.t. the stationary distributions of the Markov noise. The limit set theorem by Benaim is then used to characterize the limit sets of the recursion in terms of the dynamics of the limiting differential inclusion. We then state two variants of the Markov noise assumption under which the analysis of the recursion is similar to the one presented in this paper. Scenarios where our recursion naturally appears are presented as applications. These include controlled stochastic approximation, subgradient descent, approximate drift problem and analysis of discontinuous dynamics all in the presence of non-additive iterate-dependent Markov noise.

Item Type:Article
Source:Copyright of this article belongs to Informa UK Limited.
Keywords:Stochastic Approximation; Markov Noise; Set-valued Drift Function; Asymptotic Pseudotrajectory; Subgradient Descent.
ID Code:116462
Deposited On:12 Apr 2021 05:57
Last Modified:12 Apr 2021 05:57

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