An adaptive Metropolis-Hastings scheme: sampling and optimization

TL;DR

This paper introduces an adaptive Metropolis-Hastings algorithm that updates its proposal distribution using information-theoretic principles, improving sampling efficiency and optimization in complex energy landscapes.

Contribution

It presents a novel adaptive MH scheme that constructs an optimal mean-field approximation to the target distribution for better sampling and optimization.

Findings

Outperforms conventional MH in sampling complex distributions.

Effectively samples energy distributions in spin-glasses.

Enhances annealing optimization processes.

Abstract

We propose an adaptive Metropolis-Hastings algorithm in which sampled data are used to update the proposal distribution. We use the samples found by the algorithm at a particular step to form the information-theoretically optimal mean-field approximation to the target distribution, and update the proposal distribution to be that approximatio. We employ our algorithm to sample the energy distribution for several spin-glasses and we demonstrate the superiority of our algorithm to the conventional MH algorithm in sampling and in annealing optimization.