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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Paul Zipkin, 2008. "Old and New Methods for Lost-Sales Inventory Systems," Operations Research, INFORMS, vol. 56(5), pages 1256-1263, October.
    7. 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.
    8. 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.
    9. Emin Karagözoglu & Cagri Saglam & Agah R. Turan, 2020. "Tullock Brings Perseverance and Suspense to Tug-of-War," CESifo Working Paper Series 8103, CESifo.
    10. 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.
    11. Arthur Flajolet & Sébastien Blandin & Patrick Jaillet, 2018. "Robust Adaptive Routing Under Uncertainty," Operations Research, INFORMS, vol. 66(1), pages 210-229, January.
    12. 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.
    13. 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.
    14. Zlatana Nenova & Jennifer Shang, 2022. "Chronic Disease Progression Prediction: Leveraging Case‐Based Reasoning and Big Data Analytics," Production and Operations Management, Production and Operations Management Society, vol. 31(1), pages 259-280, January.
    15. Blai Bonet, 2007. "On the Speed of Convergence of Value Iteration on Stochastic Shortest-Path Problems," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 365-373, May.
    16. James L. Bander & Chelsea C. White, 2002. "A Heuristic Search Approach for a Nonstationary Stochastic Shortest Path Problem with Terminal Cost," Transportation Science, INFORMS, vol. 36(2), pages 218-230, May.
    17. Matsubayashi, Nobuo & Nishino, Hisakazu, 1999. "An application of Lemke's method to a class of Markov decision problems," European Journal of Operational Research, Elsevier, vol. 116(3), pages 584-590, August.
    18. Zlatana Nenova & Jennifer Shang, 2022. "Personalized Chronic Disease Follow‐Up Appointments: Risk‐Stratified Care Through Big Data," Production and Operations Management, Production and Operations Management Society, vol. 31(2), pages 583-606, February.
    19. Julio L. Ortiz, 2022. "Spread Too Thin: The Impact of Lean Inventories," International Finance Discussion Papers 1342, Board of Governors of the Federal Reserve System (U.S.).
    20. Ting-Yu Ho & Shan Liu & Zelda B. Zabinsky, 2019. "A Multi-Fidelity Rollout Algorithm for Dynamic Resource Allocation in Population Disease Management," Health Care Management Science, Springer, vol. 22(4), pages 727-755, December.

    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.