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Probabilistic decision graphs for optimization under uncertainty

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  • Finn Jensen
  • Thomas Nielsen

Abstract

This paper provides a survey on probabilistic decision graphs for modeling and solving decision problems under uncertainty. We give an introduction to influence diagrams, which is a popular framework for representing and solving sequential decision problems with a single decision maker. As the methods for solving influence diagrams can scale rather badly in the length of the decision sequence, we present a couple of approaches for calculating approximate solutions. The modeling scope of the influence diagram is limited to so-called symmetric decision problems. This limitation has motivated the development of alternative representation languages, which enlarge the class of decision problems that can be modeled efficiently. We present some of these alternative frameworks and demonstrate their expressibility using several examples. Finally, we provide a list of software systems that implement the frameworks described in the paper. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Finn Jensen & Thomas Nielsen, 2013. "Probabilistic decision graphs for optimization under uncertainty," Annals of Operations Research, Springer, vol. 204(1), pages 223-248, April.
    • Handle: RePEc:spr:annopr:v:204:y:2013:i:1:p:223-248:10.1007/s10479-012-1263-6
    DOI: 10.1007/s10479-012-1263-6
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    References listed on IDEAS

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    1. Cobb, Barry R. & Shenoy, Prakash P., 2008. "Decision making with hybrid influence diagrams using mixtures of truncated exponentials," European Journal of Operational Research, Elsevier, vol. 186(1), pages 261-275, April.
    2. Shenoy, Prakash P., 2000. "Valuation network representation and solution of asymmetric decision problems," European Journal of Operational Research, Elsevier, vol. 121(3), pages 579-608, March.
    3. Steffen L. Lauritzen & Dennis Nilsson, 2001. "Representing and Solving Decision Problems with Limited Information," Management Science, INFORMS, vol. 47(9), pages 1235-1251, September.
    4. Prakash P. Shenoy, 1992. "Valuation-Based Systems for Bayesian Decision Analysis," Operations Research, INFORMS, vol. 40(3), pages 463-484, June.
    5. Ross D. Shachter, 1986. "Evaluating Influence Diagrams," Operations Research, INFORMS, vol. 34(6), pages 871-882, December.
    6. Koller, Daphne & Milch, Brian, 2003. "Multi-agent influence diagrams for representing and solving games," Games and Economic Behavior, Elsevier, vol. 45(1), pages 181-221, October.
    7. John M. Charnes & Prakash P. Shenoy, 2004. "Multistage Monte Carlo Method for Solving Influence Diagrams Using Local Computation," Management Science, INFORMS, vol. 50(3), pages 405-418, March.
    8. Ross D. Shachter & C. Robert Kenley, 1989. "Gaussian Influence Diagrams," Management Science, INFORMS, vol. 35(5), pages 527-550, May.
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    Cited by:

    1. Manuele Leonelli & James Smith, 2015. "Bayesian decision support for complex systems with many distributed experts," Annals of Operations Research, Springer, vol. 235(1), pages 517-542, December.
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    3. Andrew J. Keith & Darryl K. Ahner, 2021. "A survey of decision making and optimization under uncertainty," Annals of Operations Research, Springer, vol. 300(2), pages 319-353, May.
    4. Manuele Leonelli & Eva Riccomagno & Jim Q. Smith, 2020. "Coherent combination of probabilistic outputs for group decision making: an algebraic approach," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(2), pages 499-528, June.

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