Competitive Collaborative Learning

We develop algorithms for a community of users to make decisions about selecting products or resources, in a model characterized by two key features: The quality of the products or resources may vary over time.Some of the users in the system may be dishonest, manipulating their actions in a Byzantine manner to achieve other goals. We formulate such learning tasks as an algorithmic problem based on the multi-armed bandit problem, but with a set of users (as opposed to a single user), of whom a constant fraction are honest and are partitioned into coalitions such that the users in a coalition perceive the same expected quality if they sample the same resource at the same time. Our main result exhibits an algorithm for this problem which converges in polylogarithmic time to a state in which the average regret (per honest user) is an arbitrarily small constant.