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Markovian Restless Bandits and Index Policies: A Review

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  • José Niño-Mora

    (Department of Statistics, Carlos III University of Madrid, 28903 Getafe, Madrid, Spain)

Abstract

The restless multi-armed bandit problem is a paradigmatic modeling framework for optimal dynamic priority allocation in stochastic models of wide-ranging applications that has been widely investigated and applied since its inception in a seminal paper by Whittle in the late 1980s. The problem has generated a vast and fast-growing literature from which a significant sample is thematically organized and reviewed in this paper. While the main focus is on priority-index policies due to their intuitive appeal, tractability, asymptotic optimality properties, and often strong empirical performance, other lines of work are also reviewed. Theoretical and algorithmic developments are discussed, along with diverse applications. The main goals are to highlight the remarkable breadth of work that has been carried out on the topic and to stimulate further research in the field.

Suggested Citation

  • José Niño-Mora, 2023. "Markovian Restless Bandits and Index Policies: A Review," Mathematics, MDPI, vol. 11(7), pages 1-27, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1639-:d:1109797
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    References listed on IDEAS

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    1. Vivek S. Borkar & Sarath Pattathil, 2022. "Whittle indexability in egalitarian processor sharing systems," Annals of Operations Research, Springer, vol. 317(2), pages 417-437, October.
    2. Dimitris Bertsimas & José Niño-Mora, 2000. "Restless Bandits, Linear Programming Relaxations, and a Primal-Dual Index Heuristic," Operations Research, INFORMS, vol. 48(1), pages 80-90, February.
    3. Banks, Jeffrey S & Sundaram, Rangarajan K, 1994. "Switching Costs and the Gittins Index," Econometrica, Econometric Society, vol. 62(3), pages 687-694, May.
    4. Roland Fryer & Philipp Harms, 2018. "Two-Armed Restless Bandits with Imperfect Information: Stochastic Control and Indexability," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 399-427, May.
    5. Daniel Adelman & Adam J. Mersereau, 2008. "Relaxations of Weakly Coupled Stochastic Dynamic Programs," Operations Research, INFORMS, vol. 56(3), pages 712-727, June.
    6. Christos H. Papadimitriou & John N. Tsitsiklis, 1999. "The Complexity of Optimal Queuing Network Control," Mathematics of Operations Research, INFORMS, vol. 24(2), pages 293-305, May.
    7. David B. Brown & James E. Smith, 2013. "Optimal Sequential Exploration: Bandits, Clairvoyants, and Wildcats," Operations Research, INFORMS, vol. 61(3), pages 644-665, June.
    8. Richard Weber, 2007. "Comments on: Dynamic priority allocation via restless bandit marginal productivity indices," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(2), pages 211-216, December.
    9. David B. Brown & James E. Smith, 2020. "Index Policies and Performance Bounds for Dynamic Selection Problems," Management Science, INFORMS, vol. 66(7), pages 3029-3050, July.
    10. P. S. Ansell & K. D. Glazebrook & J. Niño-Mora & M. O'Keeffe, 2003. "Whittle's index policy for a multi-class queueing system with convex holding costs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(1), pages 21-39, April.
    11. Xu, Jianyu & Chen, Lujie & Tang, Ou, 2021. "An online algorithm for the risk-aware restless bandit," European Journal of Operational Research, Elsevier, vol. 290(2), pages 622-639.
    12. Felipe Caro & Jérémie Gallien, 2007. "Dynamic Assortment with Demand Learning for Seasonal Consumer Goods," Management Science, INFORMS, vol. 53(2), pages 276-292, February.
    13. Meilijson, Isaac & Weiss, Gideon, 1977. "Multiple feedback at a single-server station," Stochastic Processes and their Applications, Elsevier, vol. 5(2), pages 195-205, May.
    14. Dimitris Bertsimas & José Niño-Mora, 1996. "Conservation Laws, Extended Polymatroids and Multiarmed Bandit Problems; A Polyhedral Approach to Indexable Systems," Mathematics of Operations Research, INFORMS, vol. 21(2), pages 257-306, May.
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