On stochastic gradient Langevin dynamics with dependent data streams in the logconcave case

We study the problem of sampling from a probability distribution $\pi $ on $\mathbb{R}^{d}$ which has density w.r.t. Lebesgue measure known up to normalization factor $x\mapsto \mathrm{e}^{-U(x)}/\int _{\mathbb{R}^{d}}\mathrm{e}^{-U(y)}\,\mathrm{d}y$. analyze method based Euler discretization Langevin stochastic differential equations under assumptions that potential $U$ is continuously differentiable, $\nabla U$ Lipschitz, and strongly concave. focus case where gradient log-density cannot be directly computed but unbiased estimates possibly dependent observations are available. This setting can seen as combination approximation (here gradient) type algorithms with discretized dynamics. obtain an upper bound Wasserstein-2 distance between law iterates this algorithm target constants depending explicitly Lipschitz strong convexity dimension space. Finally, weaker its in presence independent observations, we analogous results distance.