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Concentration bounds for stochastic approximations


 
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1. Title Title of document Concentration bounds for stochastic approximations
 
2. Creator Author's name, affiliation, country Noufel Frikha; Université Denis Diderot
 
2. Creator Author's name, affiliation, country Stéphane Menozzi; Universite d'Évry Val d'Essonne; France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Non asymptotic bounds, Euler scheme, Stochastic approximation algorithms, Gaussian concentration
 
3. Subject Subject classification 60H35; 65C30; 65C05
 
4. Description Abstract

We obtain non asymptotic concentration bounds for two kinds of stochastic approximations. We first consider the deviations between the expectation of a given function of an Euler like discretization scheme of some diffusion process at a fixed deterministic time and its empirical mean obtained by the Monte Carlo procedure. We then give some estimates concerning the deviation between the value at a given time-step of a stochastic approximation algorithm and its target. Under suitable assumptions both concentration bounds turn out to be Gaussian. The key tool consists in exploiting accurately the concentration properties of the increments of the schemes. Also, no specific non-degeneracy conditions are assumed.

An Erratum is available in ECP volume 17 paper number 60.
 
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7. Date (YYYY-MM-DD) 2012-10-07
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1952
 
10. Identifier Digital Object Identifier 10.1214/ECP.v17-1952
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 17
 
12. Language English=en en
 
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