### On adaptive estimation for dynamic Bernoulli bandits

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 Title: On adaptive estimation for dynamic Bernoulli bandits Authors: Lu, XAdams, NKantas, N Item Type: Journal Article Abstract: The multi-armed bandit (MAB) problem is a classic example of the exploration-exploitation dilemma. It is concerned with maximising the total rewards for a gambler by sequentially pulling an arm from a multi-armed slot machine where each arm is associated with a reward distribution. In static MABs, the reward distributions do not change over time, while in dynamic MABs, each arm's reward distribution can change, and the optimal arm can switch over time. Motivated by many real applications where rewards are binary, we focus on dynamic Bernoulli bandits. Standard methods like $\epsilon$-Greedy and Upper Confidence Bound (UCB), which rely on the sample mean estimator, often fail to track changes in the underlying reward for dynamic problems. In this paper, we overcome the shortcoming of slow response to change by deploying adaptive estimation in the standard methods and propose a new family of algorithms, which are adaptive versions of $\epsilon$-Greedy, UCB, and Thompson sampling. These new methods are simple and easy to implement. Moreover, they do not require any prior knowledge about the dynamic reward process, which is important for real applications. We examine the new algorithms numerically in different scenarios and the results show solid improvements of our algorithms in dynamic environments. Issue Date: 1-Jun-2019 Date of Acceptance: 22-May-2019 URI: http://hdl.handle.net/10044/1/70336 DOI: https://dx.doi.org/10.3934/fods.2019009 ISSN: 2639-8001 Publisher: American Institute of Mathematical Sciences Start Page: 197 End Page: 225 Journal / Book Title: Foundations of Data Science Volume: 1 Issue: 2 Copyright Statement: © 2019 American Institute of Mathematical Sciences Keywords: stat.MLstat.MLcs.LGstat.MLstat.MLcs.LG Notes: Added another AFF version of the standard UCB algorithm; modified the AFF-TS algorithm; in the numerical studies, added comparisons to SW-UCB and D-UCB Publication Status: Published Embargo Date: 2020-06-01 Appears in Collections: MathematicsStatistics