Optimal quasi-convex combinations for stochastic approximation algorithms with parallel observers

Abstract

Motivated by numerous potential applications in decentralized estimation, detection and adaptive control, Monte Carlo optimization, etc., two types of stochastic approximation (SA) algorithms with parallel observers are developed. To find the root of a non-linear function with random noise corrupted measurements, instead of employing the classical Robbins-Monro (RM) SA procedures with a single observer, a collection of physically separated parallel observers are used to estimate the same parameter. A newly formed approximation sequence is obtained by means of an appropriate quasi-convex combination of the most current values obtained from all the observers. In addition to getting strong consistency and asymptotic normality, the optimal convex combination coefficients are derived. Comparisons of asymptotic performance are made. These comparisons indicate that the algorithms suggested here are asymptotically better than the classical approach.