Abstract We study the Unadjusted Langevin Algorithm (ULA) for sampling from a probability
distribution $\nu= e^{-f} $ on $\R^ n $. We prove a convergence guarantee in Kullback …

For the task of sampling from a density $\pi\propto\exp (-V) $ on $\R^ d $, where $ V $ is
possibly non-convex but $ L $-gradient Lipschitz, we prove that averaged Langevin Monte …

Optimization algorithms and Monte Carlo sampling algorithms have provided the
computational foundations for the rapid growth in applications of statistical machine learning …

Langevin diffusion processes and their discretizations are often used for sampling from a
target density. The most convenient framework for assessing the quality of such a sampling …

We formulate gradient-based Markov chain Monte Carlo (MCMC) sampling as optimization
on the space of probability measures, with Kullback–Leibler (KL) divergence as the …

Sampling from log-concave distributions is a well researched problem that has many
applications in statistics and machine learning. We study the distributions of the form …

Abstract Underdamped Langevin Monte Carlo (ULMC) is an algorithm used to sample from
unnormalized densities by leveraging the momentum of a particle moving in a potential well …

An Euler discretization of the Langevin diffusion is known to converge to the global
minimizers of certain convex and non-convex optimization problems. We show that this …

Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising
in high-dimensional inference tasks. Here one produces an estimator of an unknown …

We study sampling from a target distribution $\nu_*= e^{-f} $ using the unadjusted Langevin
Monte Carlo (LMC) algorithm. For any potential function $ f $ whose tails behave like …