2016/07/16 by Vinayaka G. Yaji, Shalabh Bhatnagar, Yaji, Vinayaka +1 · 1 citation
Decision Sciences · Mathematics · #Advanced Bandit Algorithms Research #Advanced Optimization Algorithms Research #FOS: Electrical engineering #Markov Chains and Monte Carlo Methods #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1607.04735
openalex publication_date 2016/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the asymptotic behavior 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 in [1] 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.