Optimality in problems and optimization algorithms under indeterminacy
type: Item
instance of: scholarly article
title: Optimality in problems and optimization algorithms under indeterminacy
zbMATH Open document ID: 0603.90105
published in: Automation and Remote Control
publication date: 1986-01-01T00:00:00Z
review text: Considered is the minimization of a function \(J(x)\) on \({\mathbb{R}}^ r\) assuming that only estimates \(y(n,x)\) of the gradient \(\nabla J(x)\) can be obtained having one of the forms (a) \(y(n,x)=\nabla J(x)+\xi_ 1\) (additive noise) or (b) \(y(n,x)=Diag(\xi_ n)\nabla J(x)\) (multiplicative noise), where \((\xi_ n)\) is a sequence of independent, identically distributed, zero mean random r-vectors. Replacing \(y(n,x)\) by \(\tilde y(n,x)=\phi(y(n,x))\), formulas are given for the transformation \(\phi\) minimizing the asymptotic error covariance matrix of the resulting stochastic gradient procedure with the transformed gradient ỹ(n,x) and having an optimal gain matrix of the type \(\Gamma_ 0(n)=n^{-1}\Gamma_ 0\).
Mathematics Subject Classification ID: 90C15
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 62L20
zbMATH DE Number: 3974740
zbMATH Keywords: asymptotic error covariance matrix
zbMATH Keywords: stochastic gradient procedure
zbMATH Keywords: optimal gain matrix
author: Yakov Z. Tsypkin
reviewed by: Kurt Marti
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3974740