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A Utility Criterion for Markov Decision Processes

Author

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  • Stratton C. Jaquette

    (Systems Control, Inc., Palo Alto)

Abstract

Optimality criteria for Markov decision processes have historically been based on a risk neutral formulation of the decision maker's preferences. An explicit utility formulation, incorporating both risk and time preference and based on some results in the axiomatic theory of choice under uncertainty, is developed. This forms an optimality criterion called utility optimality with constant aversion to risk. The objective is to maximize the expected utility using an exponential utility function. Implicit in the formulation is an interpretation of the decision process which is not sequential. It is shown that optimal policies exist which are not necessarily stationary for an infinite horizon stationary Markov decision process with finite state and action spaces. An example is given.

Suggested Citation

  • Stratton C. Jaquette, 1976. "A Utility Criterion for Markov Decision Processes," Management Science, INFORMS, vol. 23(1), pages 43-49, September.
  • Handle: RePEc:inm:ormnsc:v:23:y:1976:i:1:p:43-49
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    File URL: http://dx.doi.org/10.1287/mnsc.23.1.43
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    Cited by:

    1. Rolando Cavazos-Cadena, 2010. "Optimality equations and inequalities in a class of risk-sensitive average cost Markov decision chains," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 47-84, February.
    2. Monahan, George E. & Sobel, Matthew J., 1997. "Risk-Sensitive Dynamic Market Share Attraction Games," Games and Economic Behavior, Elsevier, vol. 20(2), pages 149-160, August.
    3. Takayuki Osogami, 2012. "Iterated risk measures for risk-sensitive Markov decision processes with discounted cost," Papers 1202.3755, arXiv.org.
    4. Rolando Cavazos-Cadena, 2009. "Solutions of the average cost optimality equation for finite Markov decision chains: risk-sensitive and risk-neutral criteria," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(3), pages 541-566, December.
    5. repec:spr:compst:v:71:y:2010:i:1:p:47-84 is not listed on IDEAS
    6. repec:spr:compst:v:70:y:2009:i:3:p:541-566 is not listed on IDEAS
    7. repec:spr:compst:v:71:y:2010:i:3:p:401-425 is not listed on IDEAS
    8. Krishnamurthy Iyer & Nandyala Hemachandra, 2010. "Sensitivity analysis and optimal ultimately stationary deterministic policies in some constrained discounted cost models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(3), pages 401-425, June.
    9. Karel Sladký, 2013. "Risk-Sensitive and Mean Variance Optimality in Markov Decision Processes," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 7(3), pages 146-161, November.
    10. Bäuerle, Nicole & Jaśkiewicz, Anna, 2015. "Risk-sensitive dividend problems," European Journal of Operational Research, Elsevier, vol. 242(1), pages 161-171.

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