Transport-entropy inequalities and deviation estimates for stochastic approximation schemes

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.
Type de document :
Article dans une revue
Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2013, 18 (67), pp.1-36
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00783125
Contributeur : Noufel Frikha <>
Soumis le : jeudi 31 janvier 2013 - 14:52:45
Dernière modification le : mardi 11 octobre 2016 - 14:10:47
Document(s) archivé(s) le : mercredi 1 mai 2013 - 03:56:48

Fichiers

Transport_Entropy_stoch_scheme...
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00783125, version 1
  • ARXIV : 1301.7740

Collections

UPMC | INSMI | PMA | USPC

Citation

Max Fathi, Noufel Frikha. Transport-entropy inequalities and deviation estimates for stochastic approximation schemes. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2013, 18 (67), pp.1-36. <hal-00783125>

Partager

Métriques

Consultations de
la notice

249

Téléchargements du document

90