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We study the K-armed dueling bandit problem, a variation of the standardstochastic bandit problem where the feedback is limited to relative comparisonsof a pair of arms. The hardness of recommending Copeland winners, the arms thatbeat the greatest number of other arms, is characterized by deriving anasymptotic regret bound. We propose Copeland Winners Relative Minimum EmpiricalDivergence (CW-RMED) and derive an asymptotically optimal regret bound for it.However, it is not known whether the algorithm can be efficiently computed ornot. To address this issue, we devise an efficient version (ECW-RMED) andderive its asymptotic regret bound. Experimental comparisons of dueling banditalgorithms show that ECW-RMED significantly outperforms existing ones.

Copeland Dueling Bandit Problem: Regret Lower Bound, Optimal Algorithm, and Computationally Efficient Algorithm