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Stochastic Approximation Via Averaging: The Polyak’s Approach Revisited

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Simulation and Optimization

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

Abstract

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.

This research was supported in part by the National Science Foundation under grant DMS-9022139.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA

    G. Yin

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  1. G. Yin
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Editors and Affiliations

  1. Institut für Statistik und Informatik, Universität Wien, Universitätsstraße 5, A-1010, Wien, Austria

    Georg Pflug

  2. Institut für Statistik, Technische Universität Graz, Lessingstraße 27, A-8010, Graz, Austria

    Ulrich Dieter

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© 1992 Springer-Verlag Berlin Heidelberg

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Yin, G. (1992). Stochastic Approximation Via Averaging: The Polyak’s Approach Revisited. In: Pflug, G., Dieter, U. (eds) Simulation and Optimization. Lecture Notes in Economics and Mathematical Systems, vol 374. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48914-3_9

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  • DOI: https://doi.org/10.1007/978-3-642-48914-3_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54980-2

  • Online ISBN: 978-3-642-48914-3

  • eBook Packages: Springer Book Archive

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