IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v86y2017i1d10.1007_s00186-017-0581-5.html
   My bibliography  Save this article

Error bounds for stochastic shortest path problems

Author

Listed:
  • Eric A. Hansen

    (Mississippi State University)

Abstract

For stochastic shortest path problems, error bounds for value iteration due to Bertsekas elegantly generalize the classic MacQueen–Porteus error bounds for discounted infinite-horizon Markov decision problems, but incur prohibitive computational overhead. We derive bounds on these error bounds that can be computed with little or no overhead, making them useful in practice—especially so, since easily-computed error bounds have not previously been available for this class of problems.

Suggested Citation

  • Eric A. Hansen, 2017. "Error bounds for stochastic shortest path problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(1), pages 1-27, August.
    • Handle: RePEc:spr:mathme:v:86:y:2017:i:1:d:10.1007_s00186-017-0581-5
    DOI: 10.1007/s00186-017-0581-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00186-017-0581-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00186-017-0581-5?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. Dimitri P. Bertsekas & John N. Tsitsiklis, 1991. "An Analysis of Stochastic Shortest Path Problems," Mathematics of Operations Research, INFORMS, vol. 16(3), pages 580-595, August.
    2. Evan L. Porteus, 1975. "Bounds and Transformations for Discounted Finite Markov Decision Chains," Operations Research, INFORMS, vol. 23(4), pages 761-784, August.
    3. Chris P. Lee & Glenn M. Chertow & Stefanos A. Zenios, 2008. "Optimal Initiation and Management of Dialysis Therapy," Operations Research, INFORMS, vol. 56(6), pages 1428-1449, December.
    4. Evan L. Porteus, 1971. "Some Bounds for Discounted Sequential Decision Processes," Management Science, INFORMS, vol. 18(1), pages 7-11, September.
    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. Raymond K. Cheung & B. Muralidharan, 2000. "Dynamic Routing for Priority Shipments in LTL Service Networks," Transportation Science, INFORMS, vol. 34(1), pages 86-98, February.
    2. E. Nikolova & N. E. Stier-Moses, 2014. "A Mean-Risk Model for the Traffic Assignment Problem with Stochastic Travel Times," Operations Research, INFORMS, vol. 62(2), pages 366-382, April.
    3. Fernando Ordóñez & Nicolás E. Stier-Moses, 2010. "Wardrop Equilibria with Risk-Averse Users," Transportation Science, INFORMS, vol. 44(1), pages 63-86, February.
    4. Matthew H. Henry & Yacov Y. Haimes, 2009. "A Comprehensive Network Security Risk Model for Process Control Networks," Risk Analysis, John Wiley & Sons, vol. 29(2), pages 223-248, February.
    5. Carey E. Priebe & Donniell E. Fishkind & Lowell Abrams & Christine D. Piatko, 2005. "Random disambiguation paths for traversing a mapped hazard field," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(3), pages 285-292, April.
    6. Dimitri P. Bertsekas, 2019. "Robust shortest path planning and semicontractive dynamic programming," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(1), pages 15-37, February.
    7. Turgay Ayer & Can Zhang & Anthony Bonifonte & Anne C. Spaulding & Jagpreet Chhatwal, 2019. "Prioritizing Hepatitis C Treatment in U.S. Prisons," Operations Research, INFORMS, vol. 67(3), pages 853-873, May.
    8. A. Y. Golubin, 2003. "A Note on the Convergence of Policy Iteration in Markov Decision Processes with Compact Action Spaces," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 194-200, February.
    9. Pretolani, Daniele, 2000. "A directed hypergraph model for random time dependent shortest paths," European Journal of Operational Research, Elsevier, vol. 123(2), pages 315-324, June.
    10. Paul Zipkin, 2008. "Old and New Methods for Lost-Sales Inventory Systems," Operations Research, INFORMS, vol. 56(5), pages 1256-1263, October.
    11. M. Reza Skandari & Steven M. Shechter & Nadia Zalunardo, 2015. "Optimal Vascular Access Choice for Patients on Hemodialysis," Manufacturing & Service Operations Management, INFORMS, vol. 17(4), pages 608-619, October.
    12. Azadian, Farshid & Murat, Alper E. & Chinnam, Ratna Babu, 2012. "Dynamic routing of time-sensitive air cargo using real-time information," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(1), pages 355-372.
    13. Emin Karagözoglu & Cagri Saglam & Agah R. Turan, 2020. "Tullock Brings Perseverance and Suspense to Tug-of-War," CESifo Working Paper Series 8103, CESifo.
    14. Huizhen Yu & Dimitri Bertsekas, 2013. "Q-learning and policy iteration algorithms for stochastic shortest path problems," Annals of Operations Research, Springer, vol. 208(1), pages 95-132, September.
    15. Dolinskaya, Irina & Shi, Zhenyu (Edwin) & Smilowitz, Karen, 2018. "Adaptive orienteering problem with stochastic travel times," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 109(C), pages 1-19.
    16. Arthur Flajolet & Sébastien Blandin & Patrick Jaillet, 2018. "Robust Adaptive Routing Under Uncertainty," Operations Research, INFORMS, vol. 66(1), pages 210-229, January.
    17. Benkert, Jean-Michel & Letina, Igor & Nöldeke, Georg, 2018. "Optimal search from multiple distributions with infinite horizon," Economics Letters, Elsevier, vol. 164(C), pages 15-18.
    18. B. Curtis Eaves & Arthur F. Veinott, 2014. "Maximum-Stopping-Value Policies in Finite Markov Population Decision Chains," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 597-606, August.
    19. Daniel Lücking & Wolfgang Stadje, 2013. "The stochastic shortest-path problem for Markov chains with infinite state space with applications to nearest-neighbor lattice chains," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(2), pages 239-264, April.
    20. Mehmet U. S. Ayvaci & Oguzhan Alagoz & Elizabeth S. Burnside, 2012. "The Effect of Budgetary Restrictions on Breast Cancer Diagnostic Decisions," Manufacturing & Service Operations Management, INFORMS, vol. 14(4), pages 600-617, 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:86:y:2017:i:1:d:10.1007_s00186-017-0581-5. 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.