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

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. 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.

Authors:
 [1];  [2];  [2]
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  1. Brown Univ., Providence, RI (United States). Dept. of Chemistry
  2. Brown Univ., Providence, RI (United States). Division of Applied Mathematics
Publication Date:
Research Org.:
Brown Univ., Providence, RI (United States)
Sponsoring Org.:
USDOE Office of Science (SC); Defense Advanced Research Projects Agency (DARPA); National Science Foundation (NSF)
OSTI Identifier:
1457396
Grant/Contract Number:  
SC0010539; DMS-1317199; W911NF-15-2-0122
Resource Type:
Accepted Manuscript
Journal Name:
Applied Mathematics and Optimization
Additional Journal Information:
Journal Volume: 78; Journal Issue: 1; Journal ID: ISSN 0095-4616
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Parallel Tempering; Large Deviation Rate Function; Jump Markov Process; Empirical Measure; Ergodic Control Problem

Citation Formats

Doll, J., Dupuis, P., and Nyquist, P. A Large Deviations Analysis of Certain Qualitative Properties of Parallel Tempering and Infinite Swapping Algorithms. United States: N. p., 2017. Web. doi:10.1007/s00245-017-9401-9.
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Doll, J., Dupuis, P., & Nyquist, P. A Large Deviations Analysis of Certain Qualitative Properties of Parallel Tempering and Infinite Swapping Algorithms. United States. https://doi.org/10.1007/s00245-017-9401-9
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Doll, J., Dupuis, P., and Nyquist, P. Wed . "A Large Deviations Analysis of Certain Qualitative Properties of Parallel Tempering and Infinite Swapping Algorithms". United States. https://doi.org/10.1007/s00245-017-9401-9. https://www.osti.gov/servlets/purl/1457396.
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@article{osti_1457396,
title = {A Large Deviations Analysis of Certain Qualitative Properties of Parallel Tempering and Infinite Swapping Algorithms},
author = {Doll, J. and Dupuis, P. and Nyquist, P.},
abstractNote = {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.},
doi = {10.1007/s00245-017-9401-9},
journal = {Applied Mathematics and Optimization},
number = 1,
volume = 78,
place = {United States},
year = {Wed Feb 08 00:00:00 EST 2017},
month = {Wed Feb 08 00:00:00 EST 2017}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1007/s00245-017-9401-9
Copyright Statement
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Citation Metrics:
Cited by: 7 works
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Figures / Tables:

Figure 1 Figure 1: Assignment of dynamics due to relative heights
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Works referenced in this record:

motion
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On the Infinite Swapping Limit for Parallel Tempering
journal, January 2012

  • Dupuis, Paul; Liu, Yufei; Plattner, Nuria
  • Multiscale Modeling & Simulation, Vol. 10, Issue 3
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On the large deviation rate function for the empirical measures of reversible jump Markov processes
journal, May 2015

  • Dupuis, Paul; Liu, Yufei
  • The Annals of Probability, Vol. 43, Issue 3
  • DOI: 10.1214/13-AOP883

Rare-event sampling: Occupation-based performance measures for parallel tempering and infinite swapping Monte Carlo methods
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  • Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 47, Issue 3
  • DOI: 10.1214/10-AIHP382

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book, March 1986

On performance measures for infinite swapping Monte Carlo methods
journal, January 2015

  • Doll, J. D.; Dupuis, Paul
  • The Journal of Chemical Physics, Vol. 142, Issue 2
  • DOI: 10.1063/1.4904890
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    Works referencing / citing this record:

    Large deviations for the empirical measure of the zig-zag process
    journal, December 2021

    • Bierkens, Joris; Nyquist, Pierre; Schlottke, Mikola C.
    • The Annals of Applied Probability, Vol. 31, Issue 6
    • DOI: 10.1214/21-aap1663
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      Figures / Tables found in this record:

      Figure 1 (p. 36)figure
      Figure 2 (p. 37)figure
      Figure 3 (p. 38)figure
      Table 1 (p. 39)table
      Figure 4 (p. 40)figure
      Table 2 (p. 40)table
      Table 3 (p. 41)table
      Figure 5 (p. 42)figure
      Figure 6 (p. 43)figure
      Figure 7 (p. 43)figure
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