Complete convergence of stochastic approximation algorithm in R-d under random noises

摘要

In this article, we study a stochastic approximation algorithm that approximates the exact root theta of a function M defined in R-d into R-d. The function M cannot be known exactly, but only noisy measurements are available at each point x(n) with the error xi(n). The sequence of noise (xi(n))(n) is random; we treat both cases where it is independent and dependent and we establish the complete convergence of the approximated sequence of theta.