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arXiv · 1905.13142

On stochastic gradient Langevin dynamics with dependent data streams: the fully non-convex case

Ngoc Huy Chau·Éric Moulines·Miklos Rásonyi·Sotirios Sabanis·Ying Zhang
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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 $L^1$-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.

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Ngoc Huy Chau, Éric Moulines, Miklos Rásonyi, Sotirios Sabanis, Ying Zhang. 2019-05-30. On stochastic gradient Langevin dynamics with dependent data streams: the fully non-convex case. https://arxiv.org/abs/1905.13142

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