Zero-Inflated Bandits

• URL: http://arxiv.org/abs/2312.15595v2
• Date: Thu, 10 Oct 2024 19:17:38 GMT
• Title: Zero-Inflated Bandits
• Authors: Haoyu Wei, Runzhe Wan, Lei Shi, Rui Song,
• Abstract summary: We study zero-inflated bandits, where the reward is modeled as a classic semi-parametric distribution called zero-inflated distribution. 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.
• Score: 11.60342504007264
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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