This paper studies regret minimization in multi-armed bandits, a classical online learning problem. To develop more statistically-efficient algorithms, we propose to use the assumption of a random-effect model. In this model, the mean rewards of arms are drawn independently from an unknown distribution, whose parameters we estimate. We provide an estimator of the arm means in this model and also analyze its uncertainty. Based on these results, we design a UCB algorithm, which we call ReUCB. We analyze ReUCB and prove a Bayes regret bound on its $n$-round regret, which matches an existing lower bound. Our experiments show that ReUCB can outperform Thompson sampling in various scenarios, without assuming that the prior distribution of arm means is known.
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