  We present algorithms for reducing the Dueling Bandits problem to the
conventional (stochastic) Multi-Armed Bandits problem. The Dueling Bandits
problem is an online model of learning with ordinal feedback of the form "A is
preferred to B" (as opposed to cardinal feedback like "A has value 2.5"),
giving it wide applicability in learning from implicit user feedback and
revealed and stated preferences. In contrast to existing algorithms for the
Dueling Bandits problem, our reductions -- named $\Doubler$, $\MultiSbm$ and
$\DoubleSbm$ -- provide a generic schema for translating the extensive body of
known results about conventional Multi-Armed Bandit algorithms to the Dueling
Bandits setting. For $\Doubler$ and $\MultiSbm$ we prove regret upper bounds in
both finite and infinite settings, and conjecture about the performance of
$\DoubleSbm$ which empirically outperforms the other two as well as previous
algorithms in our experiments. In addition, we provide the first almost optimal
regret bound in terms of second order terms, such as the differences between
the values of the arms.
