  We study the non-stationary stochastic multi-armed bandit problem, where the
reward statistics of each arm may change several times during the course of
learning. The performance of a learning algorithm is evaluated in terms of
their dynamic regret, which is defined as the difference between the expected
cumulative reward of an agent choosing the optimal arm in every time step and
the cumulative reward of the learning algorithm. One way to measure the
hardness of such environments is to consider how many times the identity of the
optimal arm can change. We propose a method that achieves, in $K$-armed bandit
problems, a near-optimal $\widetilde O(\sqrt{K N(S+1)})$ dynamic regret, where
$N$ is the time horizon of the problem and $S$ is the number of times the
identity of the optimal arm changes, without prior knowledge of $S$. Previous
works for this problem obtain regret bounds that scale with the number of
changes (or the amount of change) in the reward functions, which can be much
larger, or assume prior knowledge of $S$ to achieve similar bounds.
