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Parameter Imprecision in Finite State, Finite Action Dynamic Programs

Author

Listed:
  • Chelsea C. White

    (University of Virginia, Charlottesville, Virginia)

  • Hany K. El-Deib

    (University of Virginia, Charlottesville, Virginia)

Abstract

In order to model parameter imprecision associated with a problem's reward or preference structure, we examine a finite state, finite action dynamic program having a one-step transition value-function that is affine in an imprecisely known parameter. For the finite horizon case, we also assume that the terminal value function is affine in the imprecise parameter. We assume that the parameter of interest has no dynamics, no new information about its value is received once the decision process begins, and its imprecision is described by set inclusion. We seek the set of all parameter-independent strategies that are optimal for some value of the imprecisely known parameter. We present a successive approximations procedure for solving the finite horizon case and a policy iteration procedure for determining the solution of the discounted infinite horizon case. These algorithms are then applied to a decision analysis problem with imprecise utility function and to a Markov decision process with imprecise reward structure. We also present conditions that guarantee the existence of a parameter-independent strategy that maximizes, with respect to all other parameter invariant strategies, the minimum value of its expected reward function over all possible parameter values.

Suggested Citation

  • Chelsea C. White & Hany K. El-Deib, 1986. "Parameter Imprecision in Finite State, Finite Action Dynamic Programs," Operations Research, INFORMS, vol. 34(1), pages 120-129, February.
    • Handle: RePEc:inm:oropre:v:34:y:1986:i:1:p:120-129
    DOI: 10.1287/opre.34.1.120
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    Cited by:

    1. Zhu, Zhicheng & Xiang, Yisha & Zhao, Ming & Shi, Yue, 2023. "Data-driven remanufacturing planning with parameter uncertainty," European Journal of Operational Research, Elsevier, vol. 309(1), pages 102-116.
    2. 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.
    3. Duan Li & Yacov Y. Haimes, 1988. "The uncertainty sensitivity index method (USIM) and its extension," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(6), pages 655-672, December.

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