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Selective Reviews of Bandit Problems in AI via a Statistical View

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  • Pengjie Zhou
  • Haoyu Wei
  • Huiming Zhang

Abstract

Reinforcement Learning (RL) is a widely researched area in artificial intelligence that focuses on teaching agents decision-making through interactions with their environment. A key subset includes stochastic multi-armed bandit (MAB) and continuum-armed bandit (SCAB) problems, which model sequential decision-making under uncertainty. This review outlines the foundational models and assumptions of bandit problems, explores non-asymptotic theoretical tools like concentration inequalities and minimax regret bounds, and compares frequentist and Bayesian algorithms for managing exploration-exploitation trade-offs. We also extend the discussion to $K$-armed contextual bandits and SCAB, examining their methodologies, regret analyses, and discussing the relation between the SCAB problems and the functional data analysis. Finally, we highlight recent advances and ongoing challenges in the field.

Suggested Citation

  • Pengjie Zhou & Haoyu Wei & Huiming Zhang, 2024. "Selective Reviews of Bandit Problems in AI via a Statistical View," Papers 2412.02251, arXiv.org.
  • Handle: RePEc:arx:papers:2412.02251
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    References listed on IDEAS

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    1. Hao Ji & Hans-Georg Müller, 2017. "Optimal designs for longitudinal and functional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 859-876, June.
    2. Jianqing Fan & Yongyi Guo & Mengxin Yu, 2024. "Policy Optimization Using Semiparametric Models for Dynamic Pricing," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(545), pages 552-564, January.
    3. Lalit Jain & Zhaoqi Li & Erfan Loghmani & Blake Mason & Hema Yoganarasimhan, 2024. "Effective Adaptive Exploration of Prices and Promotions in Choice-Based Demand Models," Marketing Science, INFORMS, vol. 43(5), pages 1002-1030, September.
    4. Yi Cheng & Donald A. Berry, 2007. "Optimal adaptive randomized designs for clinical trials," Biometrika, Biometrika Trust, vol. 94(3), pages 673-689.
    5. Yi Liu & Veronika Ročková, 2023. "Variable Selection Via Thompson Sampling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(541), pages 287-304, January.
    6. Haoyu Chen & Wenbin Lu & Rui Song, 2021. "Statistical Inference for Online Decision Making via Stochastic Gradient Descent," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(534), pages 708-719, April.
    7. Yao Zheng & Guang Cheng, 2021. "Finite-time analysis of vector autoregressive models under linear restrictions [Nested reduced-rank autogressive models for multiple time series]," Biometrika, Biometrika Trust, vol. 108(2), pages 469-489.
    8. Joel L. Horowitz & Sokbae Lee, 2023. "Inference in a Class of Optimization Problems: Confidence Regions and Finite Sample Bounds on Errors in Coverage Probabilities," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(3), pages 927-938, July.
    9. Kanishka Misra & Eric M. Schwartz & Jacob Abernethy, 2019. "Dynamic Online Pricing with Incomplete Information Using Multiarmed Bandit Experiments," Marketing Science, INFORMS, vol. 38(2), pages 226-252, March.
    10. Yi Chen & Yining Wang & Ethan X. Fang & Zhaoran Wang & Runze Li, 2024. "Nearly Dimension-Independent Sparse Linear Bandit over Small Action Spaces via Best Subset Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(545), pages 246-258, January.
    11. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
    12. Pavel Mozgunov & Thomas Jaki, 2020. "An information theoretic approach for selecting arms in clinical trials," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(5), pages 1223-1247, December.
    13. Sungwook Kim & Michael P. Fay & Michael A. Proschan, 2021. "Valid and approximately valid confidence intervals for current status data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(3), pages 438-452, July.
    14. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, January.
    15. Wei Qian & Ching-Kang Ing & Ji Liu, 2024. "Adaptive Algorithm for Multi-Armed Bandit Problem with High-Dimensional Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(546), pages 970-982, April.
    16. Haoyu Chen & Wenbin Lu & Rui Song, 2021. "Statistical Inference for Online Decision Making: In a Contextual Bandit Setting," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(533), pages 240-255, March.
    17. Daniel Russo & Benjamin Van Roy, 2014. "Learning to Optimize via Posterior Sampling," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1221-1243, November.
    18. Marco Battiston & Stefano Favaro & Yee Whye Teh, 2018. "Multi-Armed Bandit for Species Discovery: A Bayesian Nonparametric Approach," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 455-466, January.
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