Çoklu kollu çoklu hedefli haydutlarda dayanıklı öğrenme

Multi-objective multi-armed bandits (MO-MAB) is an important extension of the standard MAB problem that has found a wide variety of applications rang- ing from clinical trials to online recommender systems. We consider Pareto set identi cation problem in the adversarial MO-MAB setting, where at each arm pull, with probability less than 0.5, an adversary corrupts the reward samples by replacing the true samples with the samples from an arbitrary distribution of its choosing. Existing MO-MAB methods in the literature are incapable of handling such attacks unless there are strict restrictions on the contamination distributions. As a result, these methods perform poorly in practice where such restrictions on the adversary are not valid in general. To ll this gap in the literature, we propose two di erent robust, median-based optimization methods that can approximate the Pareto optimal set from contaminated samples. For the proposed methods, we prove a sample complexity bound that depends on the accuracy parameter, inverse squarely. This bound matches, in the worst case, the bounds from [1, Theorem 4] and [2, Theorem 3] that consider the adversary free setting. We compare the proposed methods with a mean-based method from the MO-MAB literature on real-world and synthetic experiments. Numerical results verify our theoretical expectations and show the importance of robust algorithm design in the adversarial setting.