On stochastic gradient Langevin dynamics with dependent data streams: the fully non-convex case
Statistics Theory
2021-02-03 v4 Probability
Machine Learning
Statistics Theory
Abstract
We consider the problem of sampling from a target distribution, which is \emph {not necessarily logconcave}, in the context of empirical risk minimization and stochastic optimization as presented in Raginsky et al. (2017). Non-asymptotic analysis results are established in the -Wasserstein distance for the behaviour of Stochastic Gradient Langevin Dynamics (SGLD) algorithms. We allow the estimation of gradients to be performed even in the presence of \emph{dependent} data streams. Our convergence estimates are sharper and \emph{uniform} in the number of iterations, in contrast to those in previous studies.
Keywords
Cite
@article{arxiv.1905.13142,
title = {On stochastic gradient Langevin dynamics with dependent data streams: the fully non-convex case},
author = {Ngoc Huy Chau and Éric Moulines and Miklos Rásonyi and Sotirios Sabanis and Ying Zhang},
journal= {arXiv preprint arXiv:1905.13142},
year = {2021}
}