On parallel processing approach to adaptive stochastic estimations

With the main motivation of improving asymptotic properties, and with reference to the recent developments on parallel stochastic approximation methods, a novel approach to adaptive Robbins-Monro stochastic approximation algorithms (1951) is developed. The authors take a previously developed algorithm as their point of departure and suggest a convex combination approach. The essence of this approach is that in lieu of using a single observer, a collection of observers which operate in parallel is used to estimate the same system. At any time, all observers take the same point of observation with possibly different noise processes. An approximation sequence Z_n is formed by taking convex combination of all the processors. A consistent procedure for constructing the best convex combination sequences is given. The proposed algorithm is proved to be asymptotically more efficient than previous approaches