Sampling from log-concave distributions is a well researched problem that has many applications in statistics and machine learning.

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 p {*}\propto\exp(-f(x)), where f:\mathbb{R} {d}\rightarrow\mathbb{R} has an L -Lipschitz gradient and is m -strongly convex. In our paper, we propose a Markov chain Monte Carlo (MCMC) algorithm based on the underdamped Langevin diffusion (ULD). Our algorithm performs significantly faster than the previously best known algorithm for solving this problem, which requires \tilde{O}\left(\kappa {1.5}/\epsilon\right) steps \cite{chen2019optimal,dalalyan2018sampling}. Moreover, our algorithm can be easily parallelized to require only O(\kappa\log\frac{1}{\epsilon}) parallel steps.

Sampling from log-concave distributions is a well researched problem that has many applications in statistics and machine learning. In our paper, we propose a Markov chain Monte Carlo (MCMC) algorithm based on the underdamped Langevin diffusion (ULD). Our algorithm performs significantly faster than the previously best known algorithm for solving this problem, which requires $\tilde{O}\left(\kappa {1.5}/\epsilon\right)$ steps \cite{chen2019optimal,dalalyan2018sampling}. Moreover, our algorithm can be easily parallelized to require only $O(\kappa\log\frac{1}{\epsilon})$ parallel steps. To solve the sampling problem, we propose a new framework to discretize stochastic differential equations. We apply this framework to discretize and simulate ULD, which converges to the target distribution $p {*}$.