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Multiconstrained Finite-Horizon Piecewise Deterministic Markov Decision Processes with Unbounded Transition Rates

Author

Listed:
  • Yonghui Huang

    (School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China)

  • Xianping Guo

    (School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China)

Abstract

This paper studies a multiconstrained problem for piecewise deterministic Markov decision processes (PDMDPs) with unbounded cost and transition rates. The goal is to minimize one type of expected finite-horizon cost over history-dependent policies while keeping some other types of expected finite-horizon costs lower than some tolerable bounds. Using the Dynkin formula for the PDMDPs, we obtain an equivalent characterization of occupancy measures and express the expected finite-horizon costs in terms of occupancy measures. Under suitable assumptions, the existence of constrained-optimal policies is shown, the linear programming formulation and its dual program for the constrained problem are derived, and the strong duality between the two programs is established. An example is provided to demonstrate our results.

Suggested Citation

  • Yonghui Huang & Xianping Guo, 2020. "Multiconstrained Finite-Horizon Piecewise Deterministic Markov Decision Processes with Unbounded Transition Rates," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 641-659, May.
    • Handle: RePEc:inm:ormoor:v:45:y:2020:i:2:p:641-659
    DOI: 10.1287/moor.2019.1005
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    References listed on IDEAS

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    1. Xianping Guo & Alexei Piunovskiy, 2011. "Discounted Continuous-Time Markov Decision Processes with Constraints: Unbounded Transition and Loss Rates," Mathematics of Operations Research, INFORMS, vol. 36(1), pages 105-132, February.
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    Cited by:

    1. Sadoghi, Amirhossein & Vecer, Jan, 2022. "Optimal liquidation problem in illiquid markets," European Journal of Operational Research, Elsevier, vol. 296(3), pages 1050-1066.
    2. Amirhossein Sadoghi & Jan Vecer, 2022. "Optimal liquidation problem in illiquid markets," Post-Print hal-03696768, HAL.

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