In this paper, we propose a Double Thompson Sampling (D-TS) algorithm for dueling bandit problems. As indicated by its name, D-TS selects both the first and the second candidates according to Thompson Sampling. Specifically, D-TS maintains a posterior distribution for the preference matrix, and chooses the pair of arms for comparison by sampling twice from the posterior distribution. This simple algorithm applies to general Copeland dueling bandits, including Condorcet dueling bandits as its

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... cial case. For general Copeland dueling bandits, we show that D-TS achieves O(K^2 T) regret. For Condorcet dueling bandits, we further simplify the D-TS algorithm and show that the simplified D-TS algorithm achieves O(K T + K^2 T) regret. Simulation results based on both synthetic and real-world data demonstrate the efficiency of the proposed D-TS algorithm.