A Large Deviations Analysis of Certain Qualitative Properties of Parallel Tempering and Infinite Swapping Algorithms

Doll, J.; Dupuis, P.; Nyquist, P.

doi:10.1007/s00245-017-9401-9

Title: A Large Deviations Analysis of Certain Qualitative Properties of Parallel Tempering and Infinite Swapping Algorithms

Journal Article · Wed Feb 08 00:00:00 EST 2017 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/s00245-017-9401-9· OSTI ID:1457396

Doll, J. ^[1]; Dupuis, P. ^[2]; Nyquist, P. ^[2]

Brown Univ., Providence, RI (United States). Dept. of Chemistry
Brown Univ., Providence, RI (United States). Division of Applied Mathematics

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. Here we show that the convergence of this diagnostic to its a priori known limit is a necessary condition for the convergence of infinite swapping. Finally, 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.

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Research Organization:: Brown Univ., Providence, RI (United States)

Sponsoring Organization:: USDOE Office of Science (SC); Defense Advanced Research Projects Agency (DARPA); National Science Foundation (NSF)

Grant/Contract Number:: SC0010539; DMS-1317199; W911NF-15-2-0122

OSTI ID:: 1457396

Journal Information:: Applied Mathematics and Optimization, Vol. 78, Issue 1; ISSN 0095-4616

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 7 works

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References (11)

motion Dupuis, Paul; Bou�, Michelle The Annals of Probability, Vol. 26, Issue 4 https://doi.org/10.1214/aop/1022855876	journal	October 1998
On the Infinite Swapping Limit for Parallel Tempering Dupuis, Paul; Liu, Yufei; Plattner, Nuria Multiscale Modeling & Simulation, Vol. 10, Issue 3 https://doi.org/10.1137/110853145	journal	January 2012
Asymptotic expansions for Markov processes with l�vy generators Fleming, W. H.; Soner, H. M. Applied Mathematics & Optimization, Vol. 19, Issue 1 https://doi.org/10.1007/BF01448199	journal	January 1989
On the large deviation rate function for the empirical measures of reversible jump Markov processes Dupuis, Paul; Liu, Yufei The Annals of Probability, Vol. 43, Issue 3 https://doi.org/10.1214/13-AOP883	journal	May 2015
Rare-event sampling: Occupation-based performance measures for parallel tempering and infinite swapping Monte Carlo methods Doll, J. D.; Plattner, Nuria; Freeman, David L. The Journal of Chemical Physics, Vol. 137, Issue 20 https://doi.org/10.1063/1.4765060	journal	November 2012
Replica Monte Carlo Simulation of Spin-Glasses Swendsen, Robert H.; Wang, Jian-Sheng Physical Review Letters, Vol. 57, Issue 21 https://doi.org/10.1103/PhysRevLett.57.2607	journal	November 1986
Exit probabilities and optimal stochastic control Fleming, Wendell H. Applied Mathematics & Optimization, Vol. 4, Issue 1 https://doi.org/10.1007/BF01442148	journal	March 1977
Variational representations for continuous time processes Budhiraja, Amarjit; Dupuis, Paul; Maroulas, Vasileios Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 47, Issue 3 https://doi.org/10.1214/10-AIHP382	journal	August 2011
Parallel tempering: Theory, applications, and new perspectives Earl, David J.; Deem, Michael W. Physical Chemistry Chemical Physics, Vol. 7, Issue 23 https://doi.org/10.1039/b509983h	journal	January 2005
Markov Processes: Characterization and Convergence Ethier, Stewart N.; Kurtz, Thomas G. https://doi.org/10.1002/9780470316658	book	March 1986
On performance measures for infinite swapping Monte Carlo methods Doll, J. D.; Dupuis, Paul The Journal of Chemical Physics, Vol. 142, Issue 2 https://doi.org/10.1063/1.4904890	journal	January 2015

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Large deviations for the empirical measure of the zig-zag process Bierkens, Joris; Nyquist, Pierre; Schlottke, Mikola C. The Annals of Applied Probability, Vol. 31, Issue 6 https://doi.org/10.1214/21-aap1663	journal	December 2021