Corruption-tolerant bandit learning

We present algorithms for solving multi-armed and linear-contextual bandit tasks in the face of adversarial corruptions in the arm responses. Traditional algorithms for solving these problems assume that nothing but mild, e.g., i.i.d. sub-Gaussian, noise disrupts an otherwise clean estimate of the utility of the arm. This assumption and the resulting approaches can fail catastrophically if there is an observant adversary that corrupts even a small fraction of the responses generated when arms are pulled. To rectify this, we propose algorithms that use recent advances in robust statistical estimation to perform arm selection in polynomial time. Our algorithms are easy to implement and vastly outperform several existing UCB and EXP-style algorithms for stochastic and adversarial multi-armed and linear-contextual bandit problems in wide variety of experimental settings. Our algorithms enjoy minimax-optimal regret bounds, as well as can tolerate an adversary that is allowed to corrupt upto a universally constant fraction of the arms pulled by the algorithm.