IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v66y2007i3p545-555.html
   My bibliography  Save this article

A structured pattern matrix algorithm for multichain Markov decision processes

Author

Listed:
  • Tetsuichiro Iki
  • Masayuki Horiguchi
  • Masami Kurano

Abstract

In this paper, we are concerned with a new algorithm for multichain finite state Markov decision processes which finds an average optimal policy through the decomposition of the state space into some communicating classes and a transient class. For each communicating class, a relatively optimal policy is found, which is used to find an optimal policy by applying the value iteration algorithm. Using a pattern matrix determining the behaviour pattern of the decision process, the decomposition of the state space is effectively done, so that the proposed algorithm simplifies the structured one given by the excellent Leizarowitz’s paper (Math Oper Res 28:553–586, 2003). Also, a numerical example is given to comprehend the algorithm. Copyright Springer-Verlag 2007

Suggested Citation

  • Tetsuichiro Iki & Masayuki Horiguchi & Masami Kurano, 2007. "A structured pattern matrix algorithm for multichain Markov decision processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 545-555, December.
    • Handle: RePEc:spr:mathme:v:66:y:2007:i:3:p:545-555
    DOI: 10.1007/s00186-006-0138-5
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-006-0138-5
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-006-0138-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Arie Leizarowitz, 2003. "An Algorithm to Identify and Compute Average Optimal Policies in Multichain Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 553-586, August.
    2. A. Hordijk & L. C. M. Kallenberg, 1979. "Linear Programming and Markov Decision Chains," Management Science, INFORMS, vol. 25(4), pages 352-362, April.
    3. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    4. Arie Hordijk & Martin L. Puterman, 1987. "On the Convergence of Policy Iteration in Finite State Undiscounted Markov Decision Processes: The Unichain Case," Mathematics of Operations Research, INFORMS, vol. 12(1), pages 163-176, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guillot, Matthieu & Stauffer, Gautier, 2020. "The Stochastic Shortest Path Problem: A polyhedral combinatorics perspective," European Journal of Operational Research, Elsevier, vol. 285(1), pages 148-158.
    2. Arie Leizarowitz & Alexander J. Zaslavski, 2007. "Uniqueness and Stability of Optimal Policies of Finite State Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 156-167, February.
    3. Pierre Bernhard & Marc Deschamps, 2017. "Kalman on dynamics and contro, Linear System Theory, Optimal Control, and Filter," Working Papers 2017-10, CRESE.
    4. Jones, Randall E. & Cacho, Oscar J., 2000. "A Dynamic Optimisation Model of Weed Control," 2000 Conference (44th), January 23-25, 2000, Sydney, Australia 123685, Australian Agricultural and Resource Economics Society.
    5. Voelkel, Michael A. & Sachs, Anna-Lena & Thonemann, Ulrich W., 2020. "An aggregation-based approximate dynamic programming approach for the periodic review model with random yield," European Journal of Operational Research, Elsevier, vol. 281(2), pages 286-298.
    6. Pam Norton & Ravi Phatarfod, 2008. "Optimal Strategies In One-Day Cricket," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 25(04), pages 495-511.
    7. Aghayi, Nazila & Maleki, Bentolhoda, 2016. "Efficiency measurement of DMUs with undesirable outputs under uncertainty based on the directional distance function: Application on bank industry," Energy, Elsevier, vol. 112(C), pages 376-387.
    8. Lodewijk Kallenberg, 2013. "Derman’s book as inspiration: some results on LP for MDPs," Annals of Operations Research, Springer, vol. 208(1), pages 63-94, September.
    9. Tan, Madeleine Sui-Lay, 2016. "Policy coordination among the ASEAN-5: A global VAR analysis," Journal of Asian Economics, Elsevier, vol. 44(C), pages 20-40.
    10. D. W. K. Yeung, 2008. "Dynamically Consistent Solution For A Pollution Management Game In Collaborative Abatement With Uncertain Future Payoffs," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 517-538.
    11. Korfhage, Thorben & Fischer-Weckemann, Björn, 2024. "Long-run consequences of informal elderly care and implications of public long-term care insurance," Journal of Health Economics, Elsevier, vol. 96(C).
    12. Crutchfield, Stephen R. & Brazee, Richard J., 1990. "An Integrated Model of Surface and Ground Water Quality," 1990 Annual meeting, August 5-8, Vancouver, Canada 271011, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    13. Hanafi, Said & Freville, Arnaud, 1998. "An efficient tabu search approach for the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 659-675, April.
    14. Schön, Cornelia & König, Eva, 2018. "A stochastic dynamic programming approach for delay management of a single train line," European Journal of Operational Research, Elsevier, vol. 271(2), pages 501-518.
    15. Eric D. Gould, 2008. "Marriage and Career: The Dynamic Decisions of Young Men," Journal of Human Capital, University of Chicago Press, vol. 2(4), pages 337-378.
    16. Lange, Rutger-Jan, 2024. "Bellman filtering and smoothing for state–space models," Journal of Econometrics, Elsevier, vol. 238(2).
    17. Renato Cordeiro Amorim, 2016. "A Survey on Feature Weighting Based K-Means Algorithms," Journal of Classification, Springer;The Classification Society, vol. 33(2), pages 210-242, July.
    18. Dmitri Blueschke & Ivan Savin, 2015. "No such thing like perfect hammer: comparing different objective function specifications for optimal control," Jena Economics Research Papers 2015-005, Friedrich-Schiller-University Jena.
    19. Sieniutycz, Stanislaw, 2015. "Synthesizing modeling of power generation and power limits in energy systems," Energy, Elsevier, vol. 84(C), pages 255-266.
    20. Jérôme Renault & Xavier Venel, 2017. "Long-Term Values in Markov Decision Processes and Repeated Games, and a New Distance for Probability Spaces," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 349-376, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:mathme:v:66:y:2007:i:3:p:545-555. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.