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May 2004 Convergence rate of linear two-time-scale stochastic approximation
Vijay R. Konda, John N. Tsitsiklis
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Ann. Appl. Probab. 14(2): 796-819 (May 2004). DOI: 10.1214/105051604000000116

Abstract

We study the rate of convergence of linear two-time-scale stochastic approximation methods. We consider two-time-scale linear iterations driven by i.i.d. noise, prove some results on their asymptotic covariance and establish asymptotic normality. The well-known result [Polyak, B. T. (1990). Automat. Remote Contr. 51 937–946; Ruppert, D. (1988). Technical Report 781, Cornell Univ. ] on the optimality of Polyak–Ruppert averaging techniques specialized to linear stochastic approximation is established as a consequence of the general results in this paper.

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Vijay R. Konda. John N. Tsitsiklis. "Convergence rate of linear two-time-scale stochastic approximation." Ann. Appl. Probab. 14 (2) 796 - 819, May 2004. https://doi.org/10.1214/105051604000000116

Information

Published: May 2004
First available in Project Euclid: 23 April 2004

zbMATH: 1094.62103
MathSciNet: MR2052903
Digital Object Identifier: 10.1214/105051604000000116

Subjects:
Primary: 62L20

Keywords: stochastic approximation , two-time-scales

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.14 • No. 2 • May 2004
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