Optimum parameters and nonasymptotic bounds on the rate of convergence of stochastic algorithms in criterial optimization problems (Q1062630)

Nonasymptotic bounds are given for the rate of convergence in the mean with respect to a functional for the Robbins-Monroe and Kiefer-Wolfowitz stochastic algorithms and for a random-search algorithm based on a statistical gradient with a pair test. The optimum parameters of the algorithms are established in the sense of maximizing the rate of decrease of the bounds as \(n\to \infty\). The investigation is carried out within the scope of broad classes of objective functionals, including convex functions and functions with power-law degeneracy.