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An online algorithm for the risk-aware restless bandit

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  • Xu, Jianyu
  • Chen, Lujie
  • Tang, Ou

Abstract

The multi-armed bandit (MAB) is a classical model for the exploration vs. exploitation trade-off. Among existing MAB models, the restless bandit model is of increasing interest because of its dynamic nature, which makes it highly applicable in practice. Like other MAB models, the traditional (risk-neutral) restless bandit model searches for the arm with the lowest mean cost and does not consider risk-aversion, which is critical in cases such as clinical trials and financial investment. This limitation thus hinders the application of the traditional restless bandit. Motivated by these concerns, we introduce a general risk measure that satisfies a mild restriction to formulate a risk-aware restless model; in particular, we set a risk measure as the criterion for the performance of each arm, instead of the expectation as in the traditional case. Compared with classical MAB models, we conclude that our model settings accommodate risk-aware researchers and decision makers. We present an index-based online algorithm for the problem, and derive an upper bound on the regret of this algorithm. Then, we conclude that our algorithm retains an instance-based regret of order O(log T/T), which is consistent with the classical MAB model. Further, some specific risk measures, namely, mean-deviation, shortfall and the discrete Kusuoka risk measure, are used to demonstrate the details of our framework.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:290:y:2021:i:2:p:622-639
    DOI: 10.1016/j.ejor.2020.08.028
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    References listed on IDEAS

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    1. Dinesh Kumar, U. & Saranga, Haritha, 2010. "Optimal selection of obsolescence mitigation strategies using a restless bandit model," European Journal of Operational Research, Elsevier, vol. 200(1), pages 170-180, January.
    2. Steven L. Scott, 2015. "Multi‐armed bandit experiments in the online service economy," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(1), pages 37-45, January.
    3. Michael Jong Kim & Andrew E.B. Lim, 2016. "Robust Multiarmed Bandit Problems," Management Science, INFORMS, vol. 62(1), pages 264-285, January.
    4. Andrzej Ruszczyński & Alexander Shapiro, 2006. "Optimization of Convex Risk Functions," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 433-452, August.
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    Cited by:

    1. José Niño-Mora, 2023. "Markovian Restless Bandits and Index Policies: A Review," Mathematics, MDPI, vol. 11(7), pages 1-27, March.
    2. Agrawal, Priyank & Tulabandhula, Theja & Avadhanula, Vashist, 2023. "A tractable online learning algorithm for the multinomial logit contextual bandit," European Journal of Operational Research, Elsevier, vol. 310(2), pages 737-750.

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