Convergence Speed and Asymptotic Distribution of a Parallel Robbins-Monro Method

Abstract

Very recently, there is a growing interest in studying parallel and distributed stochastic approximation algorithms. Previously, we suggest such an algorithm to find zeros or locate maximum values of a regression function with large state space dimension in [1], and derived the strong consistency property for that algorithm. In the present work, we concern ourselves with the problem of asymptotic properties of such an algorithm. We will study the limit behavior of the algorithm and obtain the rate of convergence and asymptotic normality results.