Stochastic Approximation Via Averaging: The Polyak’s Approach Revisited

Conference paper
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 374)


Recursive stochastic optimization algorithms are considered in this work. A class of multistage procedures is developed. We analyze essentially the same kind of procedures as proposed in Polyak’s recent work. A quite different approach is taken and correlated noise processes are dealt with. In lieu of evaluating the second moments, the methods of weak convergence are employed and the asymptotic properties are obtained by examining a suitably scaled sequence. Under rather weak conditions, we show that the algorithm via averaging is an efficient approach in that it provides us with the optimal convergence speed. In addition, no prewhitening filters are needed.


recursive estimation averaging stochastic approximation weak convergence. 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • G. Yin
    • 1
  1. 1.Department of MathematicsWayne State UniversityDetroitUSA

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