A stochastic approximation algorithm for large-dimensional systems in the Kiefer-Wolfowitz setting

The author considers the problem of finding a root of the multivariate gradient equation that arises in function maximization. When only noisy measurements of the function are available, a stochastic approximation (SA) algorithm of the general type due to Kiefer and Wolfowitz (1952) is appropriate for estimating the root. An SA algorithm is presented 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 that the algorithm can be significantly more efficient than the standard finite-difference-based algorithms in large-dimensional problems.>