Transport-entropy inequalities and deviation estimates for stochastic approximation schemes

Understand

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.