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