  We study the $K$-armed dueling bandit problem, a variation of the traditional
multi-armed bandit problem in which feedback is obtained in the form of
pairwise comparisons. Previous learning algorithms have focused on the
$\textit{fully adaptive}$ setting, where the algorithm can make updates after
every comparison. The "batched" dueling bandit problem is motivated by
large-scale applications like web search ranking and recommendation systems,
where performing sequential updates may be infeasible. In this work, we ask:
$\textit{is there a solution using only a few adaptive rounds that matches the
asymptotic regret bounds of the best sequential algorithms for $K$-armed
dueling bandits?}$ We answer this in the affirmative $\textit{under the
Condorcet condition}$, a standard setting of the $K$-armed dueling bandit
problem. We obtain asymptotic regret of $O(K^2\log^2(K)) + O(K\log(T))$ in
$O(\log(T))$ rounds, where $T$ is the time horizon. Our regret bounds nearly
match the best regret bounds known in the fully sequential setting under the
Condorcet condition. Finally, in computational experiments over a variety of
real-world datasets, we observe that our algorithm using $O(\log(T))$ rounds
achieves almost the same performance as fully sequential algorithms (that use
$T$ rounds).
