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In this paper we study the asymptotic behavior of stochastic approximationschemes with set-valued drift function and non-additive iterate-dependentMarkov noise. We show that a linearly interpolated trajectory of such arecursion is an asymptotic pseudotrajectory for the flow of a limitingdifferential inclusion obtained by averaging the set-valued drift function ofthe recursion w.r.t. the stationary distributions of the Markov noise. Thelimit set theorem in [1] is then used to characterize the limit sets of therecursion in terms of the dynamics of the limiting differential inclusion. Wethen state two variants of the Markov noise assumption under which the analysisof the recursion is similar to the one presented in this paper. Scenarios whereour recursion naturally appears are presented as applications. These includecontrolled stochastic approximation, subgradient descent, approximate driftproblem and analysis of discontinuous dynamics all in the presence ofnon-additive iterate-dependent Markov noise.

Stochastic Recursive Inclusions with Non-Additive Iterate-Dependent Markov Noise