  Adversarial attacks against stochastic multi-armed bandit (MAB) algorithms
have been extensively studied in the literature. In this work, we focus on
reward poisoning attacks and find most existing attacks can be easily detected
by our proposed detection method based on the test of homogeneity, due to their
aggressive nature in reward manipulations. This motivates us to study the
notion of stealthy attack against stochastic MABs and investigate the resulting
attackability. Our analysis shows that against two popularly employed MAB
algorithms, UCB1 and $\epsilon$-greedy, the success of a stealthy attack
depends on the environmental conditions and the realized reward of the arm
pulled in the first round. We also analyze the situation for general MAB
algorithms equipped with our attack detection method and find that it is
possible to have a stealthy attack that almost always succeeds. This brings new
insights into the security risks of MAB algorithms.
