  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.
