  We study the problem of \emph{dynamic regret minimization} in $K$-armed
Dueling Bandits under non-stationary or time varying preferences. This is an
online learning setup where the agent chooses a pair of items at each round and
observes only a relative binary `win-loss' feedback for this pair, sampled from
an underlying preference matrix at that round. We first study the problem of
static-regret minimization for adversarial preference sequences and design an
efficient algorithm with $O(\sqrt{KT})$ high probability regret. We next use
similar algorithmic ideas to propose an efficient and provably optimal
algorithm for dynamic-regret minimization under two notions of
non-stationarities. In particular, we establish $\tO(\sqrt{SKT})$ and
$\tO({V_T^{1/3}K^{1/3}T^{2/3}})$ dynamic-regret guarantees, $S$ being the total
number of `effective-switches' in the underlying preference relations and $V_T$
being a measure of `continuous-variation' non-stationarity. The complexity of
these problems have not been studied prior to this work despite the
practicability of non-stationary environments in real world systems. We justify
the optimality of our algorithms by proving matching lower bound guarantees
under both the above-mentioned notions of non-stationarities. Finally, we
corroborate our results with extensive simulations and compare the efficacy of
our algorithms over state-of-the-art baselines.
