Applications of the cross-entropy method to importance sampling and optimal control of diffusions

Please always quote using this URN: urn:nbn:de:0297-zib-49720
  • We study the cross-entropy method for diffusions. One of the results is a versatile cross-entropy algorithm that can be used to design efficient importance sampling strategies for rare events or to solve optimal control problems. The approach is based on the minimization of a suitable cross-entropy functional, with a parametric family of exponentially tilted probability distributions. We illustrate the new algorithm with several numerical examples and discuss algorithmic issues and possible extensions of the method.

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Author:Wei Zhang, Han Wang, Carsten Hartmann, Marcus Weber, Christof Schütte
Document Type:ZIB-Report
Tag:change of measure; cross-entropy method; important sampling; optimal control; rare events
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Cxx Probabilistic methods, simulation and stochastic differential equations (For theoretical aspects, see 68U20 and 60H35) / 65C05 Monte Carlo methods
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Exx Stochastic systems and control / 93E20 Optimal stochastic control
94-XX INFORMATION AND COMMUNICATION, CIRCUITS / 94Axx Communication, information / 94A17 Measures of information, entropy
Date of first Publication:2014/04/23
Series (Serial Number):ZIB-Report (14-10)
Published in:Appeared in: Siam Journal on Scientific Computing 36 (2014) A 2654-A2672

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