  We study the problem of $K$-armed dueling bandit for both stochastic and
adversarial environments, where the goal of the learner is to aggregate
information through relative preferences of pair of decisions points queried in
an online sequential manner. We first propose a novel reduction from any
(general) dueling bandits to multi-armed bandits and despite the simplicity, it
allows us to improve many existing results in dueling bandits. In particular,
\emph{we give the first best-of-both world result for the dueling bandits
regret minimization problem} -- a unified framework that is guaranteed to
perform optimally for both stochastic and adversarial preferences
simultaneously. Moreover, our algorithm is also the first to achieve an optimal
$O(\sum_{i = 1}^K \frac{\log T}{\Delta_i})$ regret bound against the
Condorcet-winner benchmark, which scales optimally both in terms of the
arm-size $K$ and the instance-specific suboptimality gaps $\{\Delta_i\}_{i =
1}^K$. This resolves the long-standing problem of designing an instancewise
gap-dependent order optimal regret algorithm for dueling bandits (with matching
lower bounds up to small constant factors). We further justify the robustness
of our proposed algorithm by proving its optimal regret rate under
adversarially corrupted preferences -- this outperforms the existing
state-of-the-art corrupted dueling results by a large margin. In summary, we
believe our reduction idea will find a broader scope in solving a diverse class
of dueling bandits setting, which are otherwise studied separately from
multi-armed bandits with often more complex solutions and worse guarantees. The
efficacy of our proposed algorithms is empirically corroborated against the
existing dueling bandit methods.
