THE WANG-LANDAU ALGORITHM REACHES THE FLAT HISTOGRAM CRITERION IN FINITE TIME

• 成果类型: Article
• 署名作者: Jacob, Pierre E.; Ryder, Robin J.
• 署名单位: National University of Singapore; Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; ENSAE Paris; Universite PSL; Universite Paris-Dauphine
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/12-AAP913
• 发表日期: 2014
• 页码: 34-53
• 关键词: general state-spaces; monte-carlo; stochastic-approximation

摘要

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.