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Importance sampling, large deviations and differential games

By Paul Dupuis and Hui Wang

Abstract

A heuristic that has emerged in the area of importance sampling is that the changes of measure used to prove large deviation lower bounds give good performance when used for importance sampling. Recent work, however, has suggested that the heuristic is incorrect in many situations. The perspective put forth in the present paper is that large deviation theory suggests many changes of measure, and that not all are suitable for importance sampling. In the setting of Cramérs Theorem, the traditional interpretation of the heuristic suggests a Þxed change of distribution on the underlying independent and identically distributed summands. In contrast, we consider importance sampling schemes where the exponential change of measure is adaptive, in the sense that it depends on the historical empirical mean. The existence of asymptotically optimal schemes within this class is demonstrated. The result indicates that an adaptive change of measure, rather tha

Year: 2004
DOI identifier: 10.1080/10451120410001733845
OAI identifier: oai:CiteSeerX.psu:10.1.1.972.1633
Provided by: CiteSeerX
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