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

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 University
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.

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

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

Grant/Contract Number:: SC0010539

OSTI ID:: 1457396

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

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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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