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Lipschitz Continuity of Value Functions in Markovian Decision Processes

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  • K. Hinderer

Abstract

We present tools and guidelines for investigating Lipschitz continuity of the value functions in MDP’s, using the Hausdorff metric and the Kantorovich metric for measuring the influence of the constraint set and the transition law, respectively. The methods are explained by examples. Additional topics include an application to the the discretization algorithm of Bertsekas (1975). Copyright Springer-Verlag Berlin Heidelberg 2005

Suggested Citation

  • K. Hinderer, 2005. "Lipschitz Continuity of Value Functions in Markovian Decision Processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(1), pages 3-22, September.
    • Handle: RePEc:spr:mathme:v:62:y:2005:i:1:p:3-22
    DOI: 10.1007/s00186-005-0438-1
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    Citations

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    Cited by:

    1. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2013. "A constructive geometrical approach to the uniqueness of Markov stationary equilibrium in stochastic games of intergenerational altruism," Journal of Economic Dynamics and Control, Elsevier, vol. 37(5), pages 1019-1039.
    2. Flavio Toxvaerd & Chryssi Giannitsarou, 2004. "Recursive global games," Money Macro and Finance (MMF) Research Group Conference 2003 104, Money Macro and Finance Research Group.
    3. Jayakumar Subramanian & Amit Sinha & Aditya Mahajan, 2023. "Robustness and Sample Complexity of Model-Based MARL for General-Sum Markov Games," Dynamic Games and Applications, Springer, vol. 13(1), pages 56-88, March.
    4. Olivier Morand & Kevin Reffett & Suchismita Tarafdar, 2018. "Generalized Envelope Theorems: Applications to Dynamic Programming," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 650-687, March.
    5. Patrick Kern & Axel Simroth & Henryk Zähle, 2020. "First-order sensitivity of the optimal value in a Markov decision model with respect to deviations in the transition probability function," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(1), pages 165-197, August.
    6. Naci Saldi & Serdar Yüksel & Tamás Linder, 2017. "On the Asymptotic Optimality of Finite Approximations to Markov Decision Processes with Borel Spaces," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 945-978, November.
    7. Yi Xiong & Ningyuan Chen & Xuefeng Gao & Xiang Zhou, 2022. "Sublinear regret for learning POMDPs," Production and Operations Management, Production and Operations Management Society, vol. 31(9), pages 3491-3504, September.

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