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February 2014 The Wang–Landau algorithm reaches the flat histogram criterion in finite time
Pierre E. Jacob, Robin J. Ryder
Ann. Appl. Probab. 24(1): 34-53 (February 2014). DOI: 10.1214/12-AAP913

Abstract

The Wang–Landau algorithm aims at sampling from a probability distribution, while penalizing some regions of the state space and favoring others. It is widely used, but its convergence properties are still unknown. We show that for some variations of the algorithm, the Wang–Landau algorithm reaches the so-called flat histogram criterion in finite time, and that this criterion can be never reached for other variations. The arguments are shown in a simple context—compact spaces, density functions bounded from both sides—for the sake of clarity, and could be extended to more general contexts.

Citation

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Pierre E. Jacob. Robin J. Ryder. "The Wang–Landau algorithm reaches the flat histogram criterion in finite time." Ann. Appl. Probab. 24 (1) 34 - 53, February 2014. https://doi.org/10.1214/12-AAP913

Information

Published: February 2014
First available in Project Euclid: 9 January 2014

zbMATH: 1288.65005
MathSciNet: MR3161640
Digital Object Identifier: 10.1214/12-AAP913

Subjects:
Primary: 60J22, 65C05
Secondary: 60J05

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.24 • No. 1 • February 2014
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