Convergence rate and averaging of nonlinear two-time-scale stochastic approximation algorithms
Abstract
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 .
Cite
@article{arxiv.math/0610329,
title = {Convergence rate and averaging of nonlinear two-time-scale stochastic approximation algorithms},
author = {Abdelkader Mokkadem and Mariane Pelletier},
journal= {arXiv preprint arXiv:math/0610329},
year = {2007}
}
Comments
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)