Electronic Journal of Probability

Transport-Entropy inequalities and deviation estimates for stochastic approximation schemes

Max Fathi and Noufel Frikha

Full-text: Open access

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.

Article information

Source
Electron. J. Probab., Volume 18 (2013), paper no. 67, 36 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465064292

Digital Object Identifier
doi:10.1214/EJP.v18-2586

Mathematical Reviews number (MathSciNet)
MR3084653

Zentralblatt MATH identifier
1284.60137

Subjects
Primary: 60H35: Computational methods for stochastic equations [See also 65C30]
Secondary: 65C30 65C05: Monte Carlo methods

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

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Fathi, Max; Frikha, Noufel. Transport-Entropy inequalities and deviation estimates for stochastic approximation schemes. Electron. J. Probab. 18 (2013), paper no. 67, 36 pp. doi:10.1214/EJP.v18-2586. https://projecteuclid.org/euclid.ejp/1465064292


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