Weighted averaging and stochastic approximation

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

Weighted averaging and stochastic approximation

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

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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)
Title of host publication	Proceedings of the IEEE Conference on Decision and Control
Editors	Anon
Volume	1
State	Published - Dec 1 1996
Externally published	Yes
Event	Proceedings of the 1996 35th IEEE Conference on Decision and Control. Part 3 (of 4) - Kobe, Jpn Duration: Dec 11 1996 → Dec 13 1996

Other

Other	Proceedings of the 1996 35th IEEE Conference on Decision and Control. Part 3 (of 4)
City	Kobe, Jpn
Period	12/11/96 → 12/13/96

All Science Journal Classification (ASJC) codes

Chemical Health and Safety
Control and Systems Engineering
Safety, Risk, Reliability and Quality

Cite this

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title = "Weighted averaging and stochastic approximation",

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.",

author = "Wang, {I. Jeng} and Chong, {Edwin K P} and Kulkarni, {Sanjeev R.}",

year = "1996",

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T1 - Weighted averaging and stochastic approximation

AU - Wang, I. Jeng

AU - Chong, Edwin K P

AU - Kulkarni, Sanjeev R.

PY - 1996/12/1

Y1 - 1996/12/1

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.

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M3 - Chapter

AN - SCOPUS:0030410969

VL - 1

BT - Proceedings of the IEEE Conference on Decision and Control

A2 - Anon, null

T2 - Proceedings of the 1996 35th IEEE Conference on Decision and Control. Part 3 (of 4)

Y2 - 11 December 1996 through 13 December 1996

ER -

Weighted averaging and stochastic approximation

Abstract

Other

All Science Journal Classification (ASJC) codes

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