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Zero-Inflated Bandits

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Listed:
  • Haoyu Wei
  • Runzhe Wan
  • Lei Shi
  • Rui Song

Abstract

Many real applications of bandits have sparse non-zero rewards, leading to slow learning speed. Using problem-specific structures for careful distribution modeling is known as critical to estimation efficiency in statistics, yet is under-explored in bandits. We initiate the study of zero-inflated bandits, where the reward is modeled as a classic semi-parametric distribution called zero-inflated distribution. We design Upper Confidence Bound- and Thompson Sampling-type algorithms for this specific structure. We derive the regret bounds under both multi-armed bandits with general reward assumptions and contextual generalized linear bandit with sub-Gaussian rewards. In many settings, the regret rates of our algorithms are either minimax optimal or state-of-the-art. The superior empirical performance of our methods is demonstrated via numerical studies.

Suggested Citation

  • Haoyu Wei & Runzhe Wan & Lei Shi & Rui Song, 2023. "Zero-Inflated Bandits," Papers 2312.15595, arXiv.org, revised Oct 2024.
  • Handle: RePEc:arx:papers:2312.15595
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    References listed on IDEAS

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    3. Bogucki, Robert, 2015. "Suprema of canonical Weibull processes," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 253-263.
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