Convergence rate and averaging of nonlinear two-time-scale stochastic approximation algorithms

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The first aim of this paper is to establish the weak convergence rate of nonlinear two-time-scale stochastic approximation algorithms. Its second aim is to introduce the averaging principle in the context of two-time-scale stochastic approximation algorithms. We first define the notion of asymptotic efficiency in this framework, then introduce the averaged two-time-scale stochastic approximation algorithm, and finally establish its weak convergence rate. We show, in particular, that both components of the averaged two-time-scale stochastic approximation algorithm simultaneously converge at the optimal rate $\sqrt{n}$.
Published at http://dx.doi.org/10.1214/105051606000000448 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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Probability, 62L20 (Primary)

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http://salesiana.dossiersoluciones.com/handle/123456789/117906

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0610329
 http://arxiv.org/abs/math/0610329
 Annals of Applied Probability 2006, Vol. 16, No. 3, 1671-1702
 doi:10.1214/105051606000000448

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