Weighted averaging and stochastic approximation

I. J. Wang; Edwin K.P. Chong; Sanjeev R. Kulkarni

doi:10.1007/BF01219775

Weighted averaging and stochastic approximation

I. J. Wang, Edwin K.P. Chong, Sanjeev R. Kulkarni

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

We explore the relationship between weighted averaging and stochastic approximation algorithms, and study their convergence via a sample-path analysis. We prove that the convergence of a stochastic approximation algorithm is equivalent to the convergence of the weighted average of the associated noise sequence. We also present necessary and sufficient noise conditions for convergence of the average of the output of a stochastic approximation algorithm in the linear case. We show that the averaged stochastic approximation algorithms can tolerate a larger class of noise sequences than the stand-alone stochastic approximation algorithms.

Original language	English (US)
Pages (from-to)	41-60
Number of pages	20
Journal	Mathematics of Control, Signals, and Systems
Volume	10
Issue number	1
DOIs	https://doi.org/10.1007/BF01219775
State	Published - 1997

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Signal Processing
Control and Optimization
Applied Mathematics

Keywords

Convergence
Necessary and sufficient noise conditions
Noise sequences
Stochastic approximation
Weighted averaging

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10.1007/BF01219775

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abstract = "We explore the relationship between weighted averaging and stochastic approximation algorithms, and study their convergence via a sample-path analysis. We prove that the convergence of a stochastic approximation algorithm is equivalent to the convergence of the weighted average of the associated noise sequence. We also present necessary and sufficient noise conditions for convergence of the average of the output of a stochastic approximation algorithm in the linear case. We show that the averaged stochastic approximation algorithms can tolerate a larger class of noise sequences than the stand-alone stochastic approximation algorithms.",

keywords = "Convergence, Necessary and sufficient noise conditions, Noise sequences, Stochastic approximation, Weighted averaging",

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T1 - Weighted averaging and stochastic approximation

AU - Wang, I. J.

AU - Chong, Edwin K.P.

AU - Kulkarni, Sanjeev R.

PY - 1997

Y1 - 1997

N2 - We explore the relationship between weighted averaging and stochastic approximation algorithms, and study their convergence via a sample-path analysis. We prove that the convergence of a stochastic approximation algorithm is equivalent to the convergence of the weighted average of the associated noise sequence. We also present necessary and sufficient noise conditions for convergence of the average of the output of a stochastic approximation algorithm in the linear case. We show that the averaged stochastic approximation algorithms can tolerate a larger class of noise sequences than the stand-alone stochastic approximation algorithms.

AB - We explore the relationship between weighted averaging and stochastic approximation algorithms, and study their convergence via a sample-path analysis. We prove that the convergence of a stochastic approximation algorithm is equivalent to the convergence of the weighted average of the associated noise sequence. We also present necessary and sufficient noise conditions for convergence of the average of the output of a stochastic approximation algorithm in the linear case. We show that the averaged stochastic approximation algorithms can tolerate a larger class of noise sequences than the stand-alone stochastic approximation algorithms.

KW - Convergence

KW - Necessary and sufficient noise conditions

KW - Noise sequences

KW - Stochastic approximation

KW - Weighted averaging

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JO - Mathematics of Control, Signals, and Systems

JF - Mathematics of Control, Signals, and Systems

IS - 1

ER -

Weighted averaging and stochastic approximation

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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