  In this paper, we present simple algorithms for Dueling Bandits. We prove
that the algorithms have regret bounds for time horizon T of order O(T^rho )
with 1/2 <= rho <= 3/4, which importantly do not depend on any preference gap
between actions, Delta. Dueling Bandits is an important extension of the
Multi-Armed Bandit problem, in which the algorithm must select two actions at a
time and only receives binary feedback for the duel outcome. This is analogous
to comparisons in which the rater can only provide yes/no or better/worse type
responses. We compare our simple algorithms to the current state-of-the-art for
Dueling Bandits, ISS and DTS, discussing complexity and regret upper bounds,
and conducting experiments on synthetic data that demonstrate their regret
performance, which in some cases exceeds state-of-the-art.
