IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v65y2007i3p519-538.html
   My bibliography  Save this article

Sample-path optimality and variance-maximization for Markov decision processes

Author

Listed:
  • Q. Zhu

Abstract

This paper studies both the average sample-path reward (ASPR) criterion and the limiting average variance criterion for denumerable discrete-time Markov decision processes. The rewards may have neither upper nor lower bounds. We give sufficient conditions on the system’s primitive data and under which we prove the existence of ASPR-optimal stationary policies and variance optimal policies. Our conditions are weaker than those in the previous literature. Moreover, our results are illustrated by a controlled queueing system. Copyright Springer-Verlag 2007

Suggested Citation

  • Q. Zhu, 2007. "Sample-path optimality and variance-maximization for Markov decision processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(3), pages 519-538, June.
    • Handle: RePEc:spr:mathme:v:65:y:2007:i:3:p:519-538
    DOI: 10.1007/s00186-006-0126-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-006-0126-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-006-0126-9?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. Keith W. Ross & Ravi Varadarajan, 1989. "Markov Decision Processes with Sample Path Constraints: The Communicating Case," Operations Research, INFORMS, vol. 37(5), pages 780-790, October.
    2. Quanxin Zhu & Xianping Guo & Yonglong Dai, 2005. "Unbounded cost Markov decision processes with limsup and liminf average criteria: new conditions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(3), pages 469-482, July.
    3. Andrzej S. Nowak, 1999. "A note on strong 1-optimal policies in Markov decision chains with unbounded costs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(3), pages 475-482, July.
    4. Arie Hordijk & Alexander A. Yushkevich, 1999. "Blackwell optimality in the class of all policies in Markov decision chains with a Borel state space and unbounded rewards," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(3), pages 421-448, December.
    5. Arie Hordijk & Alexander A. Yushkevich, 1999. "Blackwell optimality in the class of stationary policies in Markov decision chains with a Borel state space and unbounded rewards," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(1), pages 1-39, March.
    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. Nicole Leder & Bernd Heidergott & Arie Hordijk, 2010. "An Approximation Approach for the Deviation Matrix of Continuous-Time Markov Processes with Application to Markov Decision Theory," Operations Research, INFORMS, vol. 58(4-part-1), pages 918-932, August.
    2. Bernd Heidergott & Arie Hordijk & Heinz Weisshaupt, 2006. "Measure-Valued Differentiation for Stationary Markov Chains," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 154-172, February.
    3. Bernd Heidergott & Arie Hordijk & Haralambie Leahu, 2009. "Strong bounds on perturbations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(1), pages 99-127, August.
    4. Bernd Heidergott & Haralambie Leahu, 2010. "Weak Differentiability of Product Measures," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 27-51, February.
    5. Heidergott, B. & Leahu, H., 2008. "Differentiability of Product Measures," Serie Research Memoranda 0005, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    6. Yasemin Serin & Zeynep Muge Avsar, 1997. "Markov decision processes with restricted observations: Finite horizon case," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(5), pages 439-456, August.
    7. Golan, Michal & Shimkin, Nahum, 2024. "Markov decision processes with burstiness constraints," European Journal of Operational Research, Elsevier, vol. 312(3), pages 877-889.
    8. Ohlmann, Jeffrey W. & Bean, James C., 2009. "Resource-constrained management of heterogeneous assets with stochastic deterioration," European Journal of Operational Research, Elsevier, vol. 199(1), pages 198-208, November.
    9. Dmitry Krass & O. J. Vrieze, 2002. "Achieving Target State-Action Frequencies in Multichain Average-Reward Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 27(3), pages 545-566, August.
    10. Quanxin Zhu, 2007. "Average optimality inequality for continuous-time Markov decision processes in Polish spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(2), pages 299-313, October.
    11. J. Minjárez-Sosa, 2015. "Markov control models with unknown random state–action-dependent discount factors," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 743-772, 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:mathme:v:65:y:2007:i:3:p:519-538. 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.