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Asynchronous stochastic approximation with differential inclusions

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>2012
<mark>Journal</mark>Stochastic Systems
Volume2
Number of pages37
Pages (from-to)409-446
Publication StatusPublished
<mark>Original language</mark>English

Abstract

The asymptotic pseudo-trajectory approach to stochastic approximation of Benaïm, Hofbauer and Sorin is extended for asynchronous stochastic approximations with a set-valued mean field. The asynchronicity of the process is incorporated into the mean field to produce convergence results which remain similar to those of an equivalent synchronous process. In addition, this allows many of the restrictive assumptions previously associated with asynchronous stochastic approximation to be removed. The framework is extended for a coupled asynchronous stochastic approximation process with set-valued mean fields. Two-timescales arguments are used here in a similar manner to the original work in this area by Borkar. The applicability of this approach is demonstrated through learning in a Markov decision process.