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Solution to the risk-sensitive average cost optimality equation in a class of Markov decision processes with finite state space

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  • Rolando Cavazos-Cadena

Abstract

This work concerns discrete-time Markov decision processes with finite state space and bounded costs per stage. The decision maker ranks random costs via the expectation of the utility function associated to a constant risk sensitivity coefficient, and the performance of a control policy is measured by the corresponding (long-run) risk-sensitive average cost criterion. The main structural restriction on the system is the following communication assumption: For every pair of states x and y, there exists a policy π, possibly depending on x and y, such that when the system evolves under π starting at x, the probability of reaching y is positive. Within this framework, the paper establishes the existence of solutions to the optimality equation whenever the constant risk sensitivity coefficient does not exceed certain positive value. Copyright Springer-Verlag Berlin Heidelberg 2003

Suggested Citation

  • Rolando Cavazos-Cadena, 2003. "Solution to the risk-sensitive average cost optimality equation in a class of Markov decision processes with finite state space," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(2), pages 263-285, May.
    • Handle: RePEc:spr:mathme:v:57:y:2003:i:2:p:263-285
    DOI: 10.1007/s001860200256
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    Citations

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    Cited by:

    1. Daniel Hernández Hernández & Diego Hernández Bustos, 2017. "Local Poisson Equations Associated with Discrete-Time Markov Control Processes," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 1-29, April.
    2. 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.
    3. 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.
    4. Selene Chávez-Rodríguez & Rolando Cavazos-Cadena & Hugo Cruz-Suárez, 2015. "Continuity of the optimal average cost in Markov decision chains with small risk-sensitivity," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(3), pages 269-298, June.
    5. 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.
    6. Rolando Cavazos-Cadena & Raúl Montes-de-Oca, 2003. "The Value Iteration Algorithm in Risk-Sensitive Average Markov Decision Chains with Finite State Space," Mathematics of Operations Research, INFORMS, vol. 28(4), pages 752-776, November.

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