Metropolis-adjusted Subdifferential Langevin Algorithm

TL;DR

This paper introduces MASLA, a generalized MCMC algorithm that extends MALA to handle non-differentiable, non-convex, and locally Lipschitz distributions, broadening sampling applicability.

Contribution

The paper proposes MASLA, a novel algorithm that generalizes MALA to work with non-differentiable and non-convex distributions, expanding the scope of MCMC methods.

Findings

MASLA effectively samples from a broader class of distributions.

MASLA maintains computational efficiency compared to existing methods.

Experimental results show MASLA's competitive performance.

Abstract

The Metropolis-Adjusted Langevin Algorithm (MALA) is a widely used Markov Chain Monte Carlo (MCMC) method for sampling from high-dimensional distributions. However, MALA relies on differentiability assumptions that restrict its applicability. In this paper, we introduce the Metropolis-Adjusted Subdifferential Langevin Algorithm (MASLA), a generalization of MALA that extends its applicability to distributions whose log-densities are locally Lipschitz, generally non-differentiable, and non-convex. We evaluate the performance of MASLA by comparing it with other sampling algorithms in settings where they are applicable. Our results demonstrate the effectiveness of MASLA in handling a broader class of distributions while maintaining computational efficiency.