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Mean-Variance Tradeoffs in an Undiscounted MDP

Author

Listed:
  • Matthew J. Sobel

    (State University of New York at Stony Brook, Stony Brook, New York)

Abstract

A stationary policy and an initial state in an MDP (Markov decision process) induce a stationary probability distribution of the reward. The problem analyzed here is generating the Pareto optima in the sense of high mean and low variance of the stationary distribution. In the unichain case, Pareto optima can be computed either with policy improvement or with a linear program having the same number of variables and one more constraint than the formulation for gain-rate optimization. The same linear program suffices in the multichain case if the ergodic class is an element of choice.

Suggested Citation

  • Matthew J. Sobel, 1994. "Mean-Variance Tradeoffs in an Undiscounted MDP," Operations Research, INFORMS, vol. 42(1), pages 175-183, February.
    • Handle: RePEc:inm:oropre:v:42:y:1994:i:1:p:175-183
    DOI: 10.1287/opre.42.1.175
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    Cited by:

    1. René Caldentey & Martin B. Haugh, 2009. "Supply Contracts with Financial Hedging," Operations Research, INFORMS, vol. 57(1), pages 47-65, February.
    2. Jun Fei & Eugene Feinberg, 2013. "Variance minimization for constrained discounted continuous-time MDPs with exponentially distributed stopping times," Annals of Operations Research, Springer, vol. 208(1), pages 433-450, September.
    3. Li Xia, 2020. "Risk‐Sensitive Markov Decision Processes with Combined Metrics of Mean and Variance," Production and Operations Management, Production and Operations Management Society, vol. 29(12), pages 2808-2827, December.
    4. Chunling Luo & Chin Hon Tan, 2020. "Almost Stochastic Dominance for Most Risk-Averse Decision Makers," Decision Analysis, INFORMS, vol. 17(2), pages 169-184, June.
    5. Alessandro Arlotto & Noah Gans & J. Michael Steele, 2014. "Markov Decision Problems Where Means Bound Variances," Operations Research, INFORMS, vol. 62(4), pages 864-875, August.
    6. Ma, Shuai & Ma, Xiaoteng & Xia, Li, 2023. "A unified algorithm framework for mean-variance optimization in discounted Markov decision processes," European Journal of Operational Research, Elsevier, vol. 311(3), pages 1057-1067.

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