Multivariate Stochastic Approximation Using a Simultaneous Perturbation GradientApproximation

摘要

Consider the problem of finding a root of the multivariate gradient equation thatarises in function minimization. When only noisy measurements of the function are available, a stochastic approximation (SA) algorithm of the general Kiefer-Wolfowitz type is appropriate for estimating the root. This paper presents an SA algorithm that is based on a simultaneous perturbation gradient approximation instead of the standard finite difference approximation of Kiefer-Wolfowitz type procedures. Theory and numerical experience indicate p that the algorithm presented here can be significantly more efficient than the standard finite difference-based algorithms in large-dimensional problems.