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Transport-Entropy inequalities and deviation estimates for stochastic approximation schemes

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Transport-Entropy inequalities and deviation estimates for stochastic approximation schemes
2.	Creator	Author's name, affiliation, country	Max Fathi; Université Pierre & Marie Curie; France
2.	Creator	Author's name, affiliation, country	Noufel Frikha; Université Paris Diderot; France
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	deviation bounds ; transportation-entropy inequalities ; Euler scheme ; stochastic approximation algorithms ; stochastic approximation with averaging
3.	Subject	Subject classification	60H35 ; 65C30 ; 65C05
4.	Description	Abstract	We obtain new transport-entropy inequalities and, as a by-product, new deviation estimates for the laws of two kinds of discrete stochastic approximation schemes. The first one refers to the law of an Euler like discretization scheme of a diffusion process at a fixed deterministic date and the second one concerns the law of a stochastic approximation algorithm at a given time-step. Our results notably improve and complete those obtained in [Frikha, Menozzi, 2012]. The key point is to properly quantify the contribution of the diffusion term to the concentration regime. We also derive a general non-asymptotic deviation bound for the difference between a function of the trajectory of a continuous Euler scheme associated to a diffusion process and its mean. Finally, we obtain non-asymptotic bound for stochastic approximation with averaging of trajectories, in particular we prove that averaging a stochastic approximation algorithm with a slow decreasing step sequence gives rise to optimal concentration rate.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2013-07-06
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/2586
10.	Identifier	Digital Object Identifier	10.1214/EJP.v18-2586
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 18
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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