Stochastic Approximation and Its Applications to Signal Processing

Abstract

Stochastic approximation (SA) is widely applied in control, optimization, signal processing and many other areas. The aim of SA is at finding roots of an unknown function called as regression function, which can be observed but the observations are corrupted by noise. The talk starts with a brief introduction to stochastic approximation (SA) and its classical theory. In order to overcome the limitations in using classical results, an expanding truncation technique is introduced to classical SA algorithms. As results, for convergence of SA algorithms with expanding truncations no linear growth rate of the regression function nor a priori assumption of the boundedness of the estimate are required. As far as the noise condition concerned, it is the weakest possible: In fact, it is necessary in many cases. The convergence results obtained for SA algorithms with expanding truncations are then applied to stochastic optimization, to blind identification, to adaptive filtering, and to principal component analysis. In all these applications the results are obtained under much weaker conditions in comparison with existing results in literature. The talk is concluded by a few remarks.