Extensions of Kesten's Adaptive Stochastic Approximation Method

Abstract

Kesten proposed a method for adjusting the coefficients of a scalar stochastic approximation process, and proved w.p. 1 convergence. A family of multidimensional processes for function minimization are treated here. Each method consists of a sequence of truncated one-dimensional procedures of the Kesten type. The methods seem to offer a number of advantages over the usual Kiefer-Wolfowitz procedures, and are more natural analogs of the schemes in common use in deterministic optimization theory.