IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v100y1999i3d10.1023_a1022634422482.html
   My bibliography  Save this article

Single Sample Path-Based Optimization of Markov Chains

Author

Listed:
  • X. R. Cao

    (Hong Kong University Grant Council under Grant
    Hong Kong University of Science and Technology, Clear Water Bay)

Abstract

Motivated by the needs of on-line optimization of real-world engineering systems, we studied single sample path-based algorithms for Markov decision problems (MDP). The sample path used in the algorithms can be obtained by observing the operation of a real system. We give a simple example to explain the advantages of the sample path-based approach over the traditional computation-based approach: matrix inversion is not required; some transition probabilities do not have to be known; it may save storage space; and it gives the flexibility of iterating the actions for a subset of the state space in each iteration. The effect of the estimation errors and the convergence property of the sample path-based approach are studied. Finally, we propose a fast algorithm, which updates the policy whenever the system reaches a particular set of states and prove that the algorithm converges to the true optimal policy with probability one under some conditions. The sample path-based approach may have important applications to the design and management of engineering systems, such as high speed communication networks.

Suggested Citation

  • X. R. Cao, 1999. "Single Sample Path-Based Optimization of Markov Chains," Journal of Optimization Theory and Applications, Springer, vol. 100(3), pages 527-548, March.
    • Handle: RePEc:spr:joptap:v:100:y:1999:i:3:d:10.1023_a:1022634422482
    DOI: 10.1023/A:1022634422482
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1022634422482
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1022634422482?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kang Cheng & Kanjian Zhang & Shumin Fei & Haikun Wei, 2016. "Potential-Based Least-Squares Policy Iteration for a Parameterized Feedback Control System," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 692-704, May.
    2. Kang Cheng & Shumin Fei & Kanjian Zhang & Xiaomei Liu & Haikun Wei, 2014. "Temporal Difference-Based Policy Iteration for Optimal Control of Stochastic Systems," Journal of Optimization Theory and Applications, Springer, vol. 163(1), pages 165-180, October.

    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:joptap:v:100:y:1999:i:3:d:10.1023_a:1022634422482. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.