  Langevin Monte Carlo (LMC) is an iterative algorithm used to generate samples
from a distribution that is known only up to a normalizing constant. The
nonasymptotic dependence of its mixing time on the dimension and target
accuracy is understood mainly in the setting of smooth (gradient-Lipschitz)
log-densities, a serious limitation for applications in machine learning. In
this paper, we remove this limitation, providing polynomial-time convergence
guarantees for a variant of LMC in the setting of nonsmooth log-concave
distributions. At a high level, our results follow by leveraging the implicit
smoothing of the log-density that comes from a small Gaussian perturbation that
we add to the iterates of the algorithm and controlling the bias and variance
that are induced by this perturbation.
