Robust Pareto Set Identification with Contaminated Bandit Feedback

We consider the Pareto set identification (PSI) problem in multi-objective multi-armed bandits (MO-MAB) with contaminated reward observations. At each arm pull, with some probability, the true reward samples are replaced with the samples from an arbitrary contamination distribution chosen by the adversary. We propose a median-based MO-MAB algorithm for robust PSI that abides by the accuracy requirements set by the user via an accuracy parameter. We prove that the sample complexity of this algorithm depends on the accuracy parameter inverse squarely. We compare the proposed algorithm with a mean-based method from MO-MAB literature on Gaussian reward distributions. Our numerical results verify our theoretical expectations and show the necessity for robust algorithm design in the adversarial setting.