Weighted averaging and stochastic approximation
type: Item
instance of: scholarly article
title: Weighted averaging and stochastic approximation
zbMATH Open document ID: 0886.93075
DOI: 10.1007/BF01219775
author: Edwin K. P. Chong
author: Sanjeev R. Kulkarni
author: I-Jeng Wang
published in: MCSS. Mathematics of Control, Signals, and Systems
publication date: 1997-11-09T00:00:00Z
review text: The authors investigate the relations between weighted averaging and stochastic approximation (SA) algorithms. First, they define the weighted averaging operator and introduce two properties of the operator: regularity and effectiveness. They establish necessary and sufficient conditions on a sequence for convergence of its average. The equivalence between weighted averaging and SA in terms of convergence is proved, i.e., it is shown that the convergence of a weighted average of the noise sequence is necessary and sufficient for the convergence of standard SA algorithms. Based on this, they present necessary and sufficient noise conditions for convergence of averaged SA algorithms in the linear case. The established noise conditions for convergence of the averaged SA algorithms are substantially weaker than the conditions for convergence of the standard SA algorithms without averaging. The analysis is deterministic by studying the sample-path behavior of the algorithms.
Mathematics Subject Classification ID: 93E99
Mathematics Subject Classification ID: 62L20
Mathematics Subject Classification ID: 90C15
zbMATH DE Number: 1062601
zbMATH Keywords: stochastic approximation
zbMATH Keywords: weighted averaging
zbMATH Keywords: convergence
zbMATH Keywords: noise conditions
reviewed by: Katsuji Uosaki
MaRDI profile type: Publication
cites work: Convergence and robustness of the Robbins-Monro algorithm truncated at randomly varying bounds
cites work: Necessary and sufficient conditions for the Robbins-Monro method
cites work: General results on the convergence of stochastic algorithms
cites work: Q3999383
cites work: On the Averaged Stochastic Approximation for Linear Regression
cites work: Almost sure approximation of the Robbins-Monro process by sums of independent random variables
cites work: An alternative proof for convergence of stochastic approximation algorithms
cites work: Stochastic Approximation with Averaging of the Iterates: Optimal Asymptotic Rate of Convergence for General Processes
cites work: Stochastic approximation with averaging and feedback: rapidly convergent "on-line" algorithms
cites work: Stochastic approximation methods for constrained and unconstrained systems
cites work: Strong convergence of a stochastic approximation algorithm
cites work: Q4003497
cites work: Applications of a Kushner and Clark lemma to general classes of stochastic algorithms
cites work: Some Remarks on The Paper by Theodorescu and Wolff: “Sequential Estimation of Expectations in the Presence of Trend”
cites work: New method of stochastic approximation type
cites work: Acceleration of Stochastic Approximation by Averaging
cites work: Almost sure approximations to the Robbins-Monro and Kiefer-Wolfowitz processes with dependent noise
cites work: Strong representation of an adaptive stochastic approximation procedure
cites work: MINISYMPOSIUM 3
cites work: On a stochastic approximation procedure based on averaging
cites work: Convergence of the Robbins-Monro method for linear problems in a Banach space
cites work: Equivalent necessary and sufficient conditions on noise sequences for stochastic approximation algorithms
cites work: Stochastic algorithms with Armijo stepsizes for minimization of functions
cites work: On extensions of Polyak's averaging approach to stochastic approximation
cites work: Asymptotically optimal rate of convergence of smoothed stochastic recursive algorithms
full work available at URL: https://doi.org/10.1007/bf01219775
OpenAlex ID: W2172782509
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description: scientific article; zbMATH DE number 1062601