Stochastic Approximation Via Averaging: The Polyak’s Approach Revisited
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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.
Keywordsrecursive estimation averaging stochastic approximation weak convergence.
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- H.J. Kushner and D.S. Clark, Stochastic Approximation for Constrained and Unconstrained Systems, Springer-Verlag, Berlin, 1978.Google Scholar
- H.J. Kushner, Approximation and Weak Convergence Methods for Random Processes with Applications to Stochastic Systems Theory, MIT Press, Cambridge, MA, 1984.Google Scholar
- D.P. Bertsekas and J.N. Tsitsiklis, Parallel and Distributed Computing, Prentice-Hall, New Jersey, 1989.Google Scholar
- G. Yin, Recent progress in parallel stochastic approximations, to appear in Statistical Theory of Identification and Adaptive Control, (P. E. Caines and L. Gerencsér Eds.), Springer-Verlag, 1991.Google Scholar
- B. T. Polyak, New method of stochastic approximation type, Automat. Remote Control 51 (1990), 937–946.Google Scholar
- D. Ruppert, Efficient estimations from a slowly convergent Robbins-Monro process, Technical Report, No. 781, School of Oper. Res. & Industrial Eng., Cornell Univ., 1988.Google Scholar
- S.N. Ethier and T.G. Kurtz, Markov Processes, Characterization and Convergence, Wiley, New York, 1986.Google Scholar
- A. Benveniste, M. Metivier and P. Priouret, Adaptive Algorithms and Stochastic Approximation, Springer-Verlag, Berlin, 1990.Google Scholar
- W.F. Stout, Almost sure convergence, Academic Press, London, 1974.Google Scholar
- P. Billingsley, Convergence of Probability Measure, wiley, New York, 1968.Google Scholar
- H.J. Kushner and J. Yang, manuscript in preparation, 1991.Google Scholar