A Stopping Rule for Finite-Difference Stochastic Approximation

Abstract

A stopping rule is developed for finite-difference stochastic approximation (FDSA) which is to minimize an unknown objective function based on random noise corrupted observation of the function. When it is assumed that the function is convex quadratic, the necessary number of iterations for achieving a given probabilistic accuracy of the resultant solution is derived, which gives a rigorous stopping rule for FDSA. This number is polynomial in the problem size.