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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
    DOI: 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. Lucy Gongtao Chen & Daniel Zhuoyu Long & Melvyn Sim, 2015. "On Dynamic Decision Making to Meet Consumption Targets," Operations Research, INFORMS, vol. 63(5), pages 1117-1130, October.
    3. 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.
    4. Kumar, Uday M & Bhat, Sanjay P. & Kavitha, Veeraruna & Hemachandra, Nandyala, 2023. "Approximate solutions to constrained risk-sensitive Markov decision processes," European Journal of Operational Research, Elsevier, vol. 310(1), pages 249-267.
    5. Hui Chen Chiang, 2007. "Optimal prepayment behaviour," Applied Economics Letters, Taylor & Francis Journals, vol. 14(15), pages 1127-1129.
    6. 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.
    7. 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.
    8. HuiChen Chiang, 2007. "Financial intermediary's choice of borrowing," Applied Economics, Taylor & Francis Journals, vol. 40(2), pages 251-260.
    9. Rolando Cavazos-Cadena & Daniel Hernández-Hernández, 2011. "Discounted Approximations for Risk-Sensitive Average Criteria in Markov Decision Chains with Finite State Space," Mathematics of Operations Research, INFORMS, vol. 36(1), pages 133-146, February.
    10. Kerem Uğurlu & Tomasz Brzeczek, 2023. "Distorted probability operator for dynamic portfolio optimization in times of socio-economic crisis," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(4), pages 1043-1060, December.
    11. Zeynep Erkin & Matthew D. Bailey & Lisa M. Maillart & Andrew J. Schaefer & Mark S. Roberts, 2010. "Eliciting Patients' Revealed Preferences: An Inverse Markov Decision Process Approach," Decision Analysis, INFORMS, vol. 7(4), pages 358-365, December.
    12. Nicole Bäuerle & Ulrich Rieder, 2014. "More Risk-Sensitive Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 39(1), pages 105-120, February.
    13. Takayuki Osogami, 2012. "Iterated risk measures for risk-sensitive Markov decision processes with discounted cost," Papers 1202.3755, arXiv.org.
    14. 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.
    15. Sen Lin & Bo Li & Antonio Arreola-Risa & Yiwei Huang, 2023. "Optimizing a single-product production-inventory system under constant absolute risk aversion," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 510-537, October.
    16. Özlem Çavuş & Andrzej Ruszczyński, 2014. "Computational Methods for Risk-Averse Undiscounted Transient Markov Models," Operations Research, INFORMS, vol. 62(2), pages 401-417, April.
    17. Sakine Batun & Andrew J. Schaefer & Atul Bhandari & Mark S. Roberts, 2018. "Optimal Liver Acceptance for Risk-Sensitive Patients," Service Science, INFORMS, vol. 10(3), pages 320-333, September.
    18. 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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