We consider the Langevin diffusion process of the form
$dXt=−\nabla U(X_t)dt+\sqrt2\,dBt$, where $\nabla U$ is not necessarily Lipschitz continuous.
We propose a discretization scheme that converges at the specified rate
in terms of the 2-Wasserstein distance. Additionally, we demonstrate the
application of the proposed method to the problem of sampling from log-
concave distributions, a common task in machine learning. This
presentation is based on joint work with M. Benko, I. Chlebicka, and J.
Endal. For further details, see our papers:
2412.09698 and
2405.18034.