  We study a variation of the classical multi-armed bandits problem. In this
problem, the learner has to make a sequence of decisions, picking from a fixed
set of choices. In each round, she receives as feedback only the loss incurred
from the chosen action. Conventionally, this problem has been studied when
losses of the actions are drawn from an unknown distribution or when they are
adversarial. In this paper, we study this problem when the losses of the
actions also satisfy certain structural properties, and especially, do show a
trend structure. When this is true, we show that using \textit{trend
detection}, we can achieve regret of order $\tilde{O} (N \sqrt{TK})$ with
respect to a switching strategy for the version of the problem where a single
action is chosen in each round and $\tilde{O} (Nm \sqrt{TK})$ when $m$ actions
are chosen each round. This guarantee is a significant improvement over the
conventional benchmark. Our approach can, as a framework, be applied in
combination with various well-known bandit algorithms, like Exp3. For both
versions of the problem, we give regret guarantees also for the
\textit{anytime} setting, i.e. when the length of the choice-sequence is not
known in advance. Finally, we pinpoint the advantages of our method by
comparing it to some well-known other strategies.
