Does selecting the same arm has the same reward? In multi-armed bandit problem, we have a set of $K$ arms. In each round $t$, a bandit selects an arm $k$ and receives a reward $r_{kt}$. The objective is to maximize the rewards after $T$ rounds.

My question: Does selecting the same arm in two different rounds leads to the same reward? Or the rewards are completely different? 

It is surprising to me if one could select the same arm but receives a different reward and still has a sublinear regret.
In the version of the Multi-Armed Bandit problem I'm familiar with, there is a fixed list of distributions $B = R_1, R_2 \cdots R_n$, and the reward for pulling lever $k$ is chosen from the distribution $R_k$.

So pulling the same lever twice might lead to different rewards, but the rewards are connected through the distribution $R_k$.