Convergence rate and averaging of nonlinear two-time-scale stochastic approximation algorithms
成果类型：
Article
署名作者：
Mokkadem, Abdelkader; Pelletier, Mariane
署名单位：
Universite Paris Saclay
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/105051606000000448
发表日期：
2006
页码：
1671-1702
关键词：
摘要：
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-timescale stochastic approximation algorithm simultaneously converge at the optimal rate root n.
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