  The $K$-armed dueling bandit problem, where the feedback is in the form of
noisy pairwise comparisons, has been widely studied. Previous works have only
focused on the sequential setting where the policy adapts after every
comparison. However, in many applications such as search ranking and
recommendation systems, it is preferable to perform comparisons in a limited
number of parallel batches. We study the batched $K$-armed dueling bandit
problem under two standard settings: (i) existence of a Condorcet winner, and
(ii) strong stochastic transitivity and stochastic triangle inequality. For
both settings, we obtain algorithms with a smooth trade-off between the number
of batches and regret. Our regret bounds match the best known sequential regret
bounds (up to poly-logarithmic factors), using only a logarithmic number of
batches. We complement our regret analysis with a nearly-matching lower bound.
Finally, we also validate our theoretical results via experiments on synthetic
and real data.
