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Markov Decision Processes with Risk-Sensitive Criteria: An Overview

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  • Nicole Bauerle
  • Anna Ja'skiewicz

Abstract

The paper provides an overview of the theory and applications of risk-sensitive Markov decision processes. The term 'risk-sensitive' refers here to the use of the Optimized Certainty Equivalent as a means to measure expectation and risk. This comprises the well-known entropic risk measure and Conditional Value-at-Risk. We restrict our considerations to stationary problems with an infinite time horizon. Conditions are given under which optimal policies exist and solution procedures are explained. We present both the theory when the Optimized Certainty Equivalent is applied recursively as well as the case where it is applied to the cumulated reward. Discounted as well as non-discounted models are reviewed

Suggested Citation

  • Nicole Bauerle & Anna Ja'skiewicz, 2023. "Markov Decision Processes with Risk-Sensitive Criteria: An Overview," Papers 2311.06896, arXiv.org.
    • Handle: RePEc:arx:papers:2311.06896
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    References listed on IDEAS

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    1. Rolando Cavazos-Cadena & Daniel Hernández-Hernández, 2016. "A Characterization of the Optimal Certainty Equivalent of the Average Cost via the Arrow-Pratt Sensitivity Function," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 224-235, February.
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    3. Arnab Basu & Tirthankar Bhattacharyya & Vivek S. Borkar, 2008. "A Learning Algorithm for Risk-Sensitive Cost," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 880-898, November.
    4. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
    5. V. S. Borkar & S. P. Meyn, 2002. "Risk-Sensitive Optimal Control for Markov Decision Processes with Monotone Cost," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 192-209, February.
    6. Anderson, Evan W., 2005. "The dynamics of risk-sensitive allocations," Journal of Economic Theory, Elsevier, vol. 125(2), pages 93-150, December.
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