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2013 Transport-Entropy inequalities and deviation estimates for stochastic approximation schemes
Max Fathi, Noufel Frikha
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Electron. J. Probab. 18: 1-36 (2013). DOI: 10.1214/EJP.v18-2586


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.


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Max Fathi. Noufel Frikha. "Transport-Entropy inequalities and deviation estimates for stochastic approximation schemes." Electron. J. Probab. 18 1 - 36, 2013.


Accepted: 6 July 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1284.60137
MathSciNet: MR3084653
Digital Object Identifier: 10.1214/EJP.v18-2586

Primary: 60H35
Secondary: 65C05 , 65C30

Keywords: deviation bounds , Euler scheme , Stochastic approximation algorithms , stochastic approximation with averaging , transportation-entropy inequalities

Vol.18 • 2013
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