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Generalized Cross-entropy Methods with Applications to Rare-event Simulation and Optimization

Department of Mathematics The University of Queensland Brisbane 4072, Australia botev{at}maths.uq.edu.au

D.P. Kroese

Department of Mathematics The University of Queensland Brisbane 4072, Australia

T. Taimre

Department of Mathematics The University of Queensland Brisbane 4072, Australia

The cross-entropy and minimum cross-entropy methods are well-known Monte Carlo simulation techniques for rare-event probability estimation and optimization. In this paper, we investigate how these methods can be eXtended to provide a general non-parametric cross-entropy framework based on -divergence distance measures. We show how the ² distance, in particular, yields a viable alternative to the Kullback—Leibler distance. The theory is illustrated with various eXamples from density estimation, rare-event simulation and continuous multi-eXtremal optimization.

Key Words: generalized cross-entropy • maXimum entropy method • cross-entropy method • rare-event simulation • stochastic optimization • Csisár's -divergence

SIMULATION, Vol. 83, No. 11, 785-806 (2007)
DOI: 10.1177/0037549707087067


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