A Proximal Algorithm for Sampling from Non-smooth Potentials

Abstract

In this work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a polynomial-time complexity $\tilde{\mathcal{O}}(d{\epsilon }^{-1})$ to obtain $\epsilon$ total variation distance to the target density, better than most existing results under the same assumptions. Our method is based on the proximal bundle method and an alternating sampling framework. This framework requires the so-called restricted Gaussian oracle, which can be viewed as a sampling counterpart of the proximal mapping in convex optimization. One key contribution of this work is a fast algorithm that realizes the restricted Gaussian oracle for any convex non-smooth potential with bounded Lipschitz constant.

20 pages

References in corpus (7)

• Underdamped Langevin MCMC: A non-asymptotic analysis
• Convergence of Langevin MCMC in KL-divergence
• The Randomized Midpoint Method for Log-Concave Sampling
• An Efficient Sampling Algorithm for Non-smooth Composite Potentials
• Langevin Monte Carlo without smoothness
• Composite Logconcave Sampling with a Restricted Gaussian Oracle
• A proximal bundle variant with optimal iteration-complexity for a large range of prox stepsizes