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I study adversarial attacks against stochastic bandit algorithms. At eachround, the learner chooses an arm, and a stochastic reward is generated. Theadversary strategically adds corruption to the reward, and the learner is onlyable to observe the corrupted reward at each round. Two sets of results arepresented in this paper. The first set studies the optimal attack strategiesfor the adversary. The adversary has a target arm he wishes to promote, and hisgoal is to manipulate the learner into choosing this target arm $T - o(T)$times. I design attack strategies against UCB and Thompson Sampling that onlyspend $\widehat{O}(\sqrt{\log T})$ cost. Matching lower bounds are presented,and the vulnerability of UCB, Thompson sampling, and $\varepsilon$-greedy areexactly characterized. The second set studies how the learner can defendagainst the adversary. Inspired by literature on smoothed analysis andbehavioral economics, I present two simple algorithms that achieve acompetitive ratio arbitrarily close to 1.

Near Optimal Adversarial Attacks on Stochastic Bandits and Defenses with Smoothed Responses