A large deviations analysis of certain qualitative properties of parallel tempering and infinite swapping algorithms

J. Doll, P. Dupuis, P. Nyquist

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Parallel tempering, or replica exchange, is a popular method for simulating complex systems. The idea is to run parallel simulations at different temperatures, and at a given swap rate exchange configurations between the parallel simulations. From the perspective of large deviations it is optimal to let the swap rate tend to infinity and it is possible to construct a corresponding simulation scheme, known as infinite swapping. In this paper we propose a novel use of large deviations for empirical measures for a more detailed analysis of the infinite swapping limit in the setting of continuous time jump Markov processes. Using the large deviations rate function and associated stochastic control problems we consider a diagnostic based on temperature assignments, which can be easily computed during a simulation. We show that the convergence of this diagnostic to its a priori known limit is a necessary condition for the convergence of infinite swapping. The rate function is also used to investigate the impact of asymmetries in the underlying potential landscape, and where in the state space poor sampling is most likely to occur.

Original languageEnglish
Pages (from-to)103-144
JournalApplied Mathematics and Optimization
Volume78
Issue number1
DOIs
Publication statusPublished - 1 Aug 2018

Fingerprint

Parallel Tempering
Qualitative Properties
Tempering
Large Deviations
Rate Function
Parallel Simulation
Swap
Diagnostics
Markov processes
Markov Jump Processes
Large scale systems
Empirical Measures
Stochastic Control
Exchange rate
Sampling
Replica
Temperature
Asymmetry
Continuous Time
Control Problem

Cite this

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A large deviations analysis of certain qualitative properties of parallel tempering and infinite swapping algorithms. / Doll, J.; Dupuis, P.; Nyquist, P.

In: Applied Mathematics and Optimization, Vol. 78, No. 1, 01.08.2018, p. 103-144.

Research output: Contribution to journalArticleAcademicpeer-review

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