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Ordinal Dynamic Programming

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  • Matthew J. Sobel

    (Yale University)

Abstract

Numerically valued reward processes are found in most dynamic programming models. Mitten, however, recently formulated finite horizon sequential decision processes in which a real-valued reward need not be earned at each stage. Instead of the cardinality assumption implicit in past models, Mitten assumes that a decision maker has a preference order over a general collection of outcomes (which need not be numerically valued). This paper investigates infinite horizon ordinal dynamic programming models. Both deterministic and stochastic models are considered. It is shown that an optimal policy exists if and only if some stationary policy is optimal. Moreover, "policy improvement" leads to better policies using either Howard-Blackwell or Eaton-Zadeh procedures. The results illuminate the roles played by various sets of assumptions in the literature on Markovian decision processes.

Suggested Citation

  • Matthew J. Sobel, 1975. "Ordinal Dynamic Programming," Management Science, INFORMS, vol. 21(9), pages 967-975, May.
    • Handle: RePEc:inm:ormnsc:v:21:y:1975:i:9:p:967-975
    DOI: 10.1287/mnsc.21.9.967
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    Cited by:

    1. Trzaskalik, Tadeusz & Sitarz, Sebastian, 2007. "Discrete dynamic programming with outcomes in random variable structures," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1535-1548, March.
    2. Matthew Sobel, 2013. "Discounting axioms imply risk neutrality," Annals of Operations Research, Springer, vol. 208(1), pages 417-432, September.
    3. Peter A. Streufert, 2023. "Dynamic Programming for Pure-Strategy Subgame Perfection in an Arbitrary Game," Papers 2302.03855, arXiv.org, revised Mar 2023.
    4. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2017. "Does backwards induction imply subgame perfection?," Games and Economic Behavior, Elsevier, vol. 103(C), pages 19-29.
    5. Frini, Anissa & Guitouni, Adel & Martel, Jean-Marc, 2012. "A general decomposition approach for multi-criteria decision trees," European Journal of Operational Research, Elsevier, vol. 220(2), pages 452-460.
    6. Maciej Nowak & Tadeusz Trzaskalik, 2013. "Interactive procedure for a multiobjective stochastic discrete dynamic problem," Journal of Global Optimization, Springer, vol. 57(2), pages 315-330, October.
    7. Hammond, Peter J & Zank, Horst, 2013. "Rationality and Dynamic Consistency under Risk and Uncertainty," The Warwick Economics Research Paper Series (TWERPS) 1033, University of Warwick, Department of Economics.

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