Transport-entropy inequalities and deviation estimates for stochastic approximation schemes - Université Pierre et Marie Curie Accéder directement au contenu
Article Dans Une Revue Electronic Journal of Probability Année : 2013

Transport-entropy inequalities and deviation estimates for stochastic approximation schemes

Résumé

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.
Fichier principal
Vignette du fichier
Transport_Entropy_stoch_schemes.pdf (413.7 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00783125 , version 1 (31-01-2013)

Identifiants

Citer

Max Fathi, Noufel Frikha. Transport-entropy inequalities and deviation estimates for stochastic approximation schemes. Electronic Journal of Probability, 2013, 18 (67), pp.1-36. ⟨hal-00783125⟩
165 Consultations
155 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More