State dependent swap strategies and adaptive adjusting of number of temperatures in Parallel Tempering algorithms

TL;DR

This paper introduces state-dependent swap strategies and adaptive temperature adjustments in Parallel Tempering algorithms, enhancing their efficiency and flexibility for sampling complex distributions.

Contribution

It presents novel extensions to adaptive parallel tempering, including state-dependent swap strategies and online temperature adjustments, improving sampling performance.

Findings

Numerical experiments show improved sampling efficiency.

State-dependent strategies encompass standard and Equi Energy moves.

Adaptive temperature adjustment enhances algorithm robustness.

Abstract

In this paper we present extensions to the original adaptive parallel tempering algorithm. Two different approaches are presented. In the first one we introduce state-dependent strategies using current information to perform a swap step. It encompasses a wide family of potential moves including the standard one and Equi Energy type move, without any loss in tractability. In the second one, we introduce online adjustment of the number of temperatures. Numerical experiments demonstrate the effectiveness of the proposed method.