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 $\sqrt{n}$.
Citation
Abdelkader Mokkadem. Mariane Pelletier. "Convergence rate and averaging of nonlinear two-time-scale stochastic approximation algorithms." Ann. Appl. Probab. 16 (3) 1671 - 1702, August 2006. https://doi.org/10.1214/105051606000000448
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