On Mixing Times of Metropolized Algorithm With Optimization Step (MAO) : A New Framework

TL;DR

This paper introduces a new Metropolized algorithm with an optimization step (MAO) for sampling from distributions with thin tails, providing theoretical mixing time bounds and demonstrating effectiveness through simulations.

Contribution

The paper proposes the MAO algorithm, a novel method that improves sampling efficiency for challenging distributions where existing algorithms struggle, with proven mixing time bounds.

Findings

MAO effectively samples from thin-tailed distributions.

Theoretical upper bounds on MAO's mixing time are established.

Simulations validate MAO's performance across various targets.

Abstract

In this paper, we consider sampling from a class of distributions with thin tails supported on $\mathbb{R}^d$ and make two primary contributions. First, we propose a new Metropolized Algorithm With Optimization Step (MAO), which is well suited for such targets. Our algorithm is capable of sampling from distributions where the Metropolis-adjusted Langevin algorithm (MALA) is not converging or lacking in theoretical guarantees. Second, we derive upper bounds on the mixing time of MAO. Our results are supported by simulations on multiple target distributions.