Regret Guarantees for Adversarial Online Collaborative Filtering

We investigate the problem of online collaborative filtering under no-repetition constraints, whereby users need to be served content in an online fashion and a given user cannot be recommended the same content item more than once. We design and analyze a fully adaptive algorithm that works under biclustering assumptions on the user-item preference matrix, and show that this algorithm exhibits an optimal regret guarantee, while being oblivious to any prior knowledge about the sequence of users, the universe of items, as well as the biclustering parameters of the preference matrix. We further propose a more robust version of the algorithm which addresses the scenario when the preference matrix is adversarially perturbed. We then give regret guarantees that scale with the amount by which the preference matrix is perturbed from a biclustered structure. To our knowledge, these are the first results on online collaborative filtering that hold at this level of generality and adaptivity under no-repetition constraints.