WEIGHTED AVERAGING AND STOCHASTIC-APPROXIMATION

We explore the relationship between weighted averaging and stochastic approximation algorithms, and study their convergence via a sample-pat h analysis. We prove that the convergence of a stochastic approximatio n algorithm is equivalent to the convergence of the weighted average o f the associated noise sequence. We also present necessary and suffici ent noise conditions for convergence of the average of the output of a stochastic approximation algorithm in the linear case. We show that t he averaged stochastic approximation algorithms can tolerate a larger class of noise sequences than the stand-alone stochastic approximation algorithms.