Multi-Objective contextual bandits with a dominant objective

In this paper, we propose a new contextual bandit problem with two objectives, where one of the objectives dominates the other objective. Unlike single-objective bandit problems in which the learner obtains a random scalar reward for each arm it selects, in the proposed problem, the learner obtains a random reward vector, where each component of the reward vector corresponds to one of the objectives. The goal of the learner is to maximize its total reward in the non-dominant objective while ensuring that it maximizes its reward in the dominant objective. In this case, the optimal arm given a context is the one that maximizes the expected reward in the non-dominant objective among all arms that maximize the expected reward in the dominant objective. For this problem, we propose the multi-objective contextual multi-armed bandit algorithm (MOC-MAB), and prove that it achieves sublinear regret with respect to the optimal context dependent policy. Then, we compare the performance of the proposed algorithm with other state-of-the-art bandit algorithms. The proposed contextual bandit model and the algorithm have a wide range of real-world applications that involve multiple and possibly conflicting objectives ranging from wireless communication to medical diagnosis and recommender systems.