A one-measurement form of simultaneous perturbation stochastic approximation
type: Item
instance of: scholarly article
title: A one-measurement form of simultaneous perturbation stochastic approximation
zbMATH Open document ID: 0867.93086
DOI: 10.1016/S0005-1098(96)00149-5
author: James C. Spall
published in: Automatica
publication date: 1997-08-07T00:00:00Z
review text: The paper deals with the optimization problem to find \(\min L(\theta)\), where \(L(\cdot)\) is a real-valued function of a \(p\)-dimensional vector of parameters. It is assumed that the solution \(\theta^*\) can be found as root of the equation \[ g(\theta)= {{\partial L(\theta)}\over{\partial\theta}}=0 \] and, simultanously, it is assumed that only measurements of \(L(\theta)\) (typically with additive noise) are available. No direct measurements of \(g(\theta)\) (with or without noise) are available. Solution algorithms based on the gradient approximations obtained by two measurements of the loss function (regardless of the problem dimension) have been already introduced. This paper presents a form of such algorithm based on the gradient approximation obtained by one measurement of the loss function only. The new algorithm as well as the former algorithms based on two measurements (presented by the author) are analyzed in the paper. Moreover, their comparison is presented. A simple numerical example completes the paper.
Mathematics Subject Classification ID: 93E99
Mathematics Subject Classification ID: 62L20
zbMATH DE Number: 987796
zbMATH Keywords: stochastic optimization
zbMATH Keywords: gradient approximations
reviewed by: Vlasta Kaňková
MaRDI profile type: Publication
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full work available at URL: s0005-1098(96)00149-5
OpenAlex ID: W2012117977
description: scientific article; zbMATH DE number 987796