Optimum parameters and nonasymptotic bounds on the rate of convergence of stochastic algorithms in criterial optimization problems
type: Item
instance of: scholarly article
title: Optimum parameters and nonasymptotic bounds on the rate of convergence of stochastic algorithms in criterial optimization problems
zbMATH Open document ID: 0572.90086
author: Yakov Alber
author: S. V. Shil'man
published in: Automation and Remote Control
publication date: 1984-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 49M37
zbMATH DE Number: 3914100
zbMATH Keywords: Nonasymptotic bounds
zbMATH Keywords: rate of convergence in the mean
zbMATH Keywords: stochastic algorithms
zbMATH Keywords: random-search algorithm
zbMATH Keywords: optimum parameters
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3914100