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A generalized Gittins index for a Markov chain and its recursive calculation

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  • Sonin, Isaac M.

Abstract

We discuss the generalization of the classical Gittins Index for a Markov chain and propose a transparent recursive algorithm for its calculation. The foundation for this algorithm is a modified version of the Elimination algorithm proposed earlier by the author to solve the problem of optimal stopping of a Markov chain in discrete time and a finite or countable state space.

Suggested Citation

  • Sonin, Isaac M., 2008. "A generalized Gittins index for a Markov chain and its recursive calculation," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1526-1533, September.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:12:p:1526-1533
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    References listed on IDEAS

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    1. Daniel Granot & Dror Zuckerman, 1991. "Optimal Sequencing and Resource Allocation in Research and Development Projects," Management Science, INFORMS, vol. 37(2), pages 140-156, February.
    2. Isaac Sonin, 1999. "The Elimination algorithm for the problem of optimal stopping," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(1), pages 111-123, March.
    3. Eric V. Denardo & Uriel G. Rothblum & Ludo Van der Heyden, 2004. "Index Policies for Stochastic Search in a Forest with an Application to R&D Project Management," Mathematics of Operations Research, INFORMS, vol. 29(1), pages 162-181, February.
    4. Michael N. Katehakis & Arthur F. Veinott, 1987. "The Multi-Armed Bandit Problem: Decomposition and Computation," Mathematics of Operations Research, INFORMS, vol. 12(2), pages 262-268, May.
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    Cited by:

    1. Isaac M. Sonin & Constantine Steinberg, 2016. "Continue, quit, restart probability model," Annals of Operations Research, Springer, vol. 241(1), pages 295-318, June.
    2. Esther Frostig & Gideon Weiss, 2016. "Four proofs of Gittins’ multiarmed bandit theorem," Annals of Operations Research, Springer, vol. 241(1), pages 127-165, June.
    3. Isaac M. Sonin & Konstantin Sonin, 2020. "A Continuous-Time Model of Financial Clearing," Working Papers 2020-101, Becker Friedman Institute for Research In Economics.
    4. Eric Denardo & Eugene Feinberg & Uriel Rothblum, 2013. "The multi-armed bandit, with constraints," Annals of Operations Research, Springer, vol. 208(1), pages 37-62, September.
    5. José Niño-Mora, 2020. "A Fast-Pivoting Algorithm for Whittle’s Restless Bandit Index," Mathematics, MDPI, vol. 8(12), pages 1-21, December.
    6. Amod J. Basnet & Isaac M. Sonin, 2022. "Parallel computing for Markov chains with islands and ports," Annals of Operations Research, Springer, vol. 317(2), pages 335-352, October.
    7. Nicolas Gast & Bruno Gaujal & Kimang Khun, 2023. "Testing indexability and computing Whittle and Gittins index in subcubic time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(3), pages 391-436, June.
    8. Isaac M. Sonin & Konstantin Sonin, 2017. "Banks as Tanks: A Continuous-Time Model of Financial Clearing," Papers 1705.05943, arXiv.org, revised Jul 2020.
    9. Malekipirbazari, Milad & Çavuş, Özlem, 2024. "Index policy for multiarmed bandit problem with dynamic risk measures," European Journal of Operational Research, Elsevier, vol. 312(2), pages 627-640.

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