Weighted averaging and stochastic approximation

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

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


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 languageAmerican English
Pages (from-to)41-60
Number of pages20
JournalMathematics of Control, Signals, and Systems
Issue number1
StatePublished - 1997

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Control and Optimization
  • Applied Mathematics


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


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