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Motivated by applications of bandit algorithms in education, we consider astochastic multi-armed bandit problem with $\varepsilon$-contaminated rewards.We allow an adversary to give arbitrary unbounded contaminated rewards withfull knowledge of the past and future. We impose the constraint that for eachtime $t$ the proportion of contaminated rewards for any action is less than orequal to $\varepsilon$. We derive concentration inequalities for two robustmean estimators for sub-Gaussian distributions in the$\varepsilon$-contamination context. We define the $\varepsilon$-contaminatedstochastic bandit problem and use our robust mean estimators to give twovariants of a robust Upper Confidence Bound (UCB) algorithm, crUCB. Usingregret derived from only the underlying stochastic rewards, both variants ofcrUCB achieve $\mathcal{O} (\sqrt{KT\log T})$ regret for small enoughcontamination proportions. Our simulations assume small horizons, reflectingthe newly explored setting of bandits in education. We show that in certainadversarial regimes crUCB not only outperforms algorithms designed forstochastic (UCB1) and adversarial (EXP3) bandits but also those that have "bestof both worlds" guarantees (EXP3++ and TsallisInf) even when our constraint onthe proportion of contaminated rewards is broken.

What You See May Not Be What You Get: UCB Bandit Algorithms Robust to {\epsilon}-Contamination