Skip to main content
SpringerLink
Log in

Sensitive Criteria in Markov Decision Processes with a Borel State Space

  • Conference paper
Operations Research Proceedings 1994

Part of the book series: Operations Research Proceedings ((ORP,volume 1994))

  • 175 Accesses

Summary

The paper considers Markov decision processes with a Borel state space, finite action sets, bounded rewards, and a bounded transition density satisfying a simultaneous Doeblin-type recurrence condition. The existence of stationary strong 0-discount optimal and Blackwell optimal policies is proved. A characterization of those policies in terms of the average optimality equation (the infinite dimensional lexicographical optimality equation, respectively) is given.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Blackwell D. Discrete dynamic programming. Ann. Math. Stat. 33 (1962), 719–726.

    Article  Google Scholar 

  2. Veinott A.F. Jr. Discrete dynamic programming with sensitive optimality criteria. Ann. Math. Stat. 40 (1969), 1635–1660.

    Article  Google Scholar 

  3. Sladky K. On the set of optimal controls for Markov chains with rewards. Kybemetika 10 (1974), 350–367.

    Google Scholar 

  4. Dekker R. and Hordijk A. Average, sensitive and Blackwell optimal policies in denumerable Markov decision chains with unbounded rewards. Math. Oper. Res. 13 (1988), 395–420.

    Article  Google Scholar 

  5. Cavazos-Cadena R. and Lasserre J.B. Strong 1-optimal stationary policies in denumerable Markov decision processes. System Control Letters 11 (1988), 65–71.

    Article  Google Scholar 

  6. Yushkevich A.A. Blackwell optimal policies in a Markov decision process with a Borel state space. Technical report 94-2, UNC-Chaxlotte, Dept. of Mathematics (submitted to Z. Oper. Res.).

    Google Scholar 

  7. Yushkevich A.A. Strong 0-discount optimal policies in a Maxkov decision process with a Borel state space. Technical report 94-3, UNC-Charlotte, Dept. of Mathematics.

    Google Scholar 

  8. Dynkin E.B. and Yushkevich A.A. Controlled Markov Processes. Springer-Verlag, Berlin-Heidelberg-New York 1979 (Grundlehren der mathematischen Wissenschaften 235).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Charlotte, USA

    Alexander Yushkevich

Authors
  1. Alexander Yushkevich
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Wirtschaftsinformatik und Operations Research, Universität zu Köln, Pohligstraße 1, D-50969, Köln, Germany

    Ulrich Derigs (Lehrstuhl) (Lehrstuhl)

  2. Mathematisches Institut, Universität zu Köln, Weyertal 80, D-50931, Köln, Germany

    Achim Bachem

  3. Institut für Betriebswirtschaftslehre, Christian-Albrechts-Universität zu Kiel, Olshausenstraße 40, D-24118, Kiel, Germany

    Andreas Drexl

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Yushkevich, A. (1995). Sensitive Criteria in Markov Decision Processes with a Borel State Space. In: Derigs, U., Bachem, A., Drexl, A. (eds) Operations Research Proceedings 1994. Operations Research Proceedings, vol 1994. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79459-9_45

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-79459-9_45

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58793-4

  • Online ISBN: 978-3-642-79459-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation