Annals of Operations Research

, Volume 134, Issue 1, pp 19–67 | Cite as

A Tutorial on the Cross-Entropy Method

  • Pieter-Tjerk de Boer
  • Dirk P. Kroese
  • Shie Mannor
  • Reuven Y. Rubinstein


The cross-entropy (CE) method is a new generic approach to combinatorial and multi-extremal optimization and rare event simulation. The purpose of this tutorial is to give a gentle introduction to the CE method. We present the CE methodology, the basic algorithm and its modifications, and discuss applications in combinatorial optimization and machine learning.

Key words

cross-entropy method Monte-Carlo simulation randomized optimization machine learning rare events 


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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Pieter-Tjerk de Boer
    • 1
  • Dirk P. Kroese
    • 2
  • Shie Mannor
    • 3
  • Reuven Y. Rubinstein
    • 4
  1. 1.Department of Electrical Engineering, Mathematics and Computer ScienceUniversity of TwenteEnschedeThe Netherlands
  2. 2.Department of MathematicsThe University of QueenslandBrisbaneAustralia
  3. 3.Department of Electrical and Computer EngineeringMcGill UniversityMontrealCanada
  4. 4.Department of Industrial Engineering, TechnionIsrael Institute of TechnologyHaifaIsrael

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