  We prove quantitative convergence rates at which discrete Langevin-like
processes converge to the invariant distribution of a related stochastic
differential equation. We study the setup where the additive noise can be
non-Gaussian and state-dependent and the potential function can be non-convex.
We show that the key properties of these processes depend on the potential
function and the second moment of the additive noise. We apply our theoretical
findings to studying the convergence of Stochastic Gradient Descent (SGD) for
non-convex problems and corroborate them with experiments using SGD to train
deep neural networks on the CIFAR-10 dataset.
