Robust Pareto Set Identification with Contaminated Bandit Feedback

Abstract: 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 fixed probability, the true reward samples are replaced with the samples from an arbitrary contamination distribution chosen by an adversary. We consider ({\alpha}, {\delta})-PAC PSI and propose a sample median-based multi-objective adaptive elimination algorithm that returns an ({\alpha}, {\delta})- PAC Pareto set upon termination with a sample complexity bound that depends on the contamination probability. As the contamination probability decreases, we recover the wellknown sample complexity results in MO-MAB. We compare the proposed algorithm with a mean-based method from MO-MAB literature, as well as an extended version that uses median estimators, on several PSI problems under adversarial corruptions, including review bombing and diabetes management. Our numerical results support our theoretical findings and demonstrate that robust algorithm design is crucial for accurate PSI under contaminated reward observations.