Unichain and Aperiodicity Are Sufficient for Asymptotic Optimality of Average-Reward Restless Bandits

Published Online:https://doi.org/10.1287/moor.2024.0678

References

  • [1] Bertsimas D, Niño Mora J (2000) Restless bandits, linear programming relaxations, and a primal-dual index heuristic. Oper. Res. 48(1):80–90.LinkGoogle Scholar
  • [2] Brown DB, Smith JE (2020) Index policies and performance bounds for dynamic selection problems. Management Sci. 66(7):3029–3050.LinkGoogle Scholar
  • [3] Brown DB, Zhang J (2022) Dynamic programs with shared resources and signals: Dynamic fluid policies and asymptotic optimality. Oper. Res. 70(5):3015–3033.LinkGoogle Scholar
  • [4] Brown DB, Zhang J (2025) Fluid policies, reoptimization, and performance guarantees in dynamic resource allocation. Oper. Res. 73(2):1029–1045.LinkGoogle Scholar
  • [5] D’Aeth JC, Ghosal S, Grimm F, Haw D, Koca E, Lau K, Liu H, et al. (2023) Optimal hospital care scheduling during the SARS-CoV-2 pandemic. Management Sci. 69(10):5923–5947.LinkGoogle Scholar
  • [6] Durrett R (2019) Probability: Theory and Examples, 5th ed. (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • [7] Gast N, Gaujal B, Khun K (2023) Testing indexability and computing Whittle and Gittins index in subcubic time. Math. Methods Oper. Res. 97(3):391–436.CrossrefGoogle Scholar
  • [8] Gast N, Gaujal B, Yan C (2020) Exponential convergence rate for the asymptotic optimality of Whittle index policy. Preprint, submitted December 16, https://arxiv.org/abs/2012.09064.Google Scholar
  • [9] Gast N, Gaujal B, Yan C (2023) Exponential asymptotic optimality of Whittle index policy. Queueing Systems 104(1):107–150.CrossrefGoogle Scholar
  • [10] Gast N, Gaujal B, Yan C (2024) Linear program-based policies for restless bandits: Necessary and sufficient conditions for (exponentially fast) asymptotic optimality. Math. Oper. Res. 49(4):2468–2491.LinkGoogle Scholar
  • [11] Gast N, Gaujal B, Yan C (2024) Reoptimization nearly solves weakly coupled Markov decision processes. Preprint, submitted May 6, https://arxiv.org/abs/2211.01961.Google Scholar
  • [12] Ghosh A, Nagaraj D, Jain M, Tambe M (2023) Indexability is not enough for Whittle: Improved, near-optimal algorithms for restless bandits. Proc. Internat. Conf. Autonomous Agents Multiagent Systems (International Foundation for Autonomous Agents and Multiagent Systems, Richland, SC), 1294–1302.Google Scholar
  • [13] Goldsztajn D, Avrachenkov K (2024) Asymptotically optimal policies for weakly coupled Markov decision processes. Preprint, submitted December 6, https://arxiv.org/abs/2406.04751.Google Scholar
  • [14] Hawkins JT (2003) A Langrangian decomposition approach to weakly coupled dynamic optimization problems and its applications. PhD thesis, Massachusetts Institute of Technology, Cambridge.Google Scholar
  • [15] Hong Y, Xie Q, Chen Y, Wang W (2023) Restless bandits with average reward: Breaking the uniform global attractor assumption. Adv. Neural Inform. Processing Systems 36:12810–12844.Google Scholar
  • [16] Hong Y, Xie Q, Chen Y, Wang W (2024) Achieving exponential asymptotic optimality in average-reward restless bandits without global attractor assumption. Preprint, submitted October 17, https://arxiv.org/abs/2405.17882.Google Scholar
  • [17] Hong Y, Xie Q, Chen Y, Wang W (2024) Unichain and aperiodicity are sufficient for asymptotic optimality of average-reward restless bandits. https://github.com/YigeHong/rb-focus-set/.Google Scholar
  • [18] Hu W, Frazier P (2017) An asymptotically optimal index policy for finite-horizon restless bandits. Preprint, submitted July 1, https://arxiv.org/abs/1707.00205.Google Scholar
  • [19] Niño-Mora J (2023) Markovian restless bandits and index policies: A review. Mathematics 11(7):1639.CrossrefGoogle Scholar
  • [20] Papadimitriou CH, Tsitsiklis JN (1999) The complexity of optimal queuing network control. Math. Oper. Res. 24(2):293–305.LinkGoogle Scholar
  • [21] Puterman ML (2005) Markov Decision Processes: Discrete Stochastic Dynamic Programming (John Wiley & Sons, Hoboken, NJ).Google Scholar
  • [22] Verloop IM (2016) Asymptotically optimal priority policies for indexable and nonindexable restless bandits. Ann. Appl. Probab. 26(4):1947–1995.CrossrefGoogle Scholar
  • [23] Weber RR, Weiss G (1990) On an index policy for restless bandits. J. Appl. Probab. 27(3):637–648.CrossrefGoogle Scholar
  • [24] Whittle P (1988) Restless bandits: Activity allocation in a changing world. J. Appl. Probab. 25:287–298.CrossrefGoogle Scholar
  • [25] Yan C (2024) An optimal-control approach to infinite-horizon restless bandits: Achieving asymptotic optimality with minimal assumptions. Proc. IEEE Conf. Decision Control CDC (IEEE, Piscataway, NJ), 6665–6672.Google Scholar
  • [26] Zayas-Cabán G, Jasin S, Wang G (2019) An asymptotically optimal heuristic for general nonstationary finite-horizon restless multi-armed, multi-action bandits. Adv. Appl. Probab. 51:745–772.CrossrefGoogle Scholar
  • [27] Zhang X, Frazier PI (2021) Restless bandits with many arms: Beating the central limit theorem. Preprint, submitted July 25, https://arxiv.org/abs/2107.11911.Google Scholar
  • [28] Zhang X, Frazier PI (2022) Near-optimality for infinite-horizon restless bandits with many arms. Preprint, submitted March 29, https://arxiv.org/abs/2203.15853.Google Scholar
  • [29] Zhang X, Hong Y, Wang W (2025) Projection-based Lyapunov method for fully heterogeneous weakly-coupled MDPs. Preprint, submitted February 9, https://arxiv.org/abs/2502.06072.Google Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.