  We study the non-stationary dueling bandits problem with $K$ arms, where the
time horizon $T$ consists of $M$ stationary segments, each of which is
associated with its own preference matrix. The learner repeatedly selects a
pair of arms and observes a binary preference between them as feedback. To
minimize the accumulated regret, the learner needs to pick the Condorcet winner
of each stationary segment as often as possible, despite preference matrices
and segment lengths being unknown. We propose the $\mathrm{Beat\, the\,
Winner\, Reset}$ algorithm and prove a bound on its expected binary weak regret
in the stationary case, which tightens the bound of current state-of-art
algorithms. We also show a regret bound for the non-stationary case, without
requiring knowledge of $M$ or $T$. We further propose and analyze two
meta-algorithms, $\mathrm{DETECT}$ for weak regret and $\mathrm{Monitored\,
Dueling\, Bandits}$ for strong regret, both based on a detection-window
approach that can incorporate any dueling bandit algorithm as a black-box
algorithm. Finally, we prove a worst-case lower bound for expected weak regret
in the non-stationary case.
