Thompson Sampling Algorithms for Mean-Variance Bandits

• URL: http://arxiv.org/abs/2002.00232v3
• Date: Mon, 3 Aug 2020 13:34:15 GMT
• Title: Thompson Sampling Algorithms for Mean-Variance Bandits
• Authors: Qiuyu Zhu and Vincent Y. F. Tan
• Abstract summary: We develop Thompson Sampling-style algorithms for mean-variance MAB. We also provide comprehensive regret analyses for Gaussian and Bernoulli bandits. Our algorithms significantly outperform existing LCB-based algorithms for all risk tolerances.
• Score: 97.43678751629189
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The multi-armed bandit (MAB) problem is a classical learning task that exemplifies the exploration-exploitation tradeoff. However, standard formulations do not take into account {\em risk}. In online decision making systems, risk is a primary concern. In this regard, the mean-variance risk measure is one of the most common objective functions. Existing algorithms for mean-variance optimization in the context of MAB problems have unrealistic assumptions on the reward distributions. We develop Thompson Sampling-style algorithms for mean-variance MAB and provide comprehensive regret analyses for Gaussian and Bernoulli bandits with fewer assumptions. Our algorithms achieve the best known regret bounds for mean-variance MABs and also attain the information-theoretic bounds in some parameter regimes. Empirical simulations show that our algorithms significantly outperform existing LCB-based algorithms for all risk tolerances.

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