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We propose $\tt RandUCB$, a bandit strategy that builds on theoreticallyderived confidence intervals similar to upper confidence bound (UCB)algorithms, but akin to Thompson sampling (TS), it uses randomization to tradeoff exploration and exploitation. In the $K$-armed bandit setting, we show thatthere are infinitely many variants of $\tt RandUCB$, all of which achieve theminimax-optimal $\widetilde{O}(\sqrt{K T})$ regret after $T$ rounds. Moreover,for a specific multi-armed bandit setting, we show that both UCB and TS can berecovered as special cases of $\tt RandUCB$. For structured bandits, where eacharm is associated with a $d$-dimensional feature vector and rewards aredistributed according to a linear or generalized linear model, we prove that$\tt RandUCB$ achieves the minimax-optimal $\widetilde{O}(d \sqrt{T})$ regreteven in the case of infinitely many arms. Through experiments in both themulti-armed and structured bandit settings, we demonstrate that $\tt RandUCB$matches or outperforms TS and other randomized exploration strategies. Ourtheoretical and empirical results together imply that $\tt RandUCB$ achievesthe best of both worlds.

Old Dog Learns New Tricks: Randomized UCB for Bandit Problems