@article{EJP2586,
author = {Max Fathi and Noufel Frikha},
title = {Transport-Entropy inequalities and deviation estimates for stochastic approximation schemes},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {18},
year = {2013},
keywords = {deviation bounds ; transportation-entropy inequalities ; Euler scheme ; stochastic approximation algorithms ; stochastic approximation with averaging},
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.},
pages = {no. 67, 1-36},
issn = {1083-6489},
doi = {10.1214/EJP.v18-2586},
url = {http://ejp.ejpecp.org/article/view/2586}}