Convergence rate of linear two-time-scale stochastic approximation

Vijay R. Konda; John N. Tsitsiklis

doi:10.1214/105051604000000116

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Convergence rate of linear two-time-scale stochastic approximation

Vijay R. Konda·John N. Tsitsiklis

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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. 2004-05-14. Convergence rate of linear two-time-scale stochastic approximation. https://doi.org/10.1214/105051604000000116

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