  Contextual bandit algorithms are applied in a wide range of domains, from
advertising to recommender systems, from clinical trials to education. In many
of these domains, malicious agents may have incentives to attack the bandit
algorithm to induce it to perform a desired behavior. For instance, an
unscrupulous ad publisher may try to increase their own revenue at the expense
of the advertisers; a seller may want to increase the exposure of their
products, or thwart a competitor's advertising campaign. In this paper, we
study several attack scenarios and show that a malicious agent can force a
linear contextual bandit algorithm to pull any desired arm $T - o(T)$ times
over a horizon of $T$ steps, while applying adversarial modifications to either
rewards or contexts that only grow logarithmically as $O(\log T)$. We also
investigate the case when a malicious agent is interested in affecting the
behavior of the bandit algorithm in a single context (e.g., a specific user).
We first provide sufficient conditions for the feasibility of the attack and we
then propose an efficient algorithm to perform the attack. We validate our
theoretical results on experiments performed on both synthetic and real-world
datasets.
