Transport-Entropy inequalities and deviation estimates for stochastic approximations schemes
نویسندگان
چکیده
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 [10]. The key point is to properly quantify the contribution of the diffusion term to the concentration regime. We also derive a general nonasymptotic 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.
منابع مشابه
Transport-entropy inequalities and deviation estimates for stochastic approximation schemes
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