Competitive collaborative learning

Intuitively, it is clear that trust or shared taste enables a community of users to make better decisions over time, by learning cooperatively and avoiding one another's mistakes. However, it is also clear that the presence of malicious, dishonest users in the community threatens the usefulness of such collaborative learning processes. We investigate this issue by developing algorithms for a multi-user online learning problem in which each user makes a sequence of decisions about selecting products or resources. Our model, which generalizes the adversarial multi-armed bandit problem, is characterized by two key features:(1)The quality of the products or resources may vary over time.(2)Some of the users in the system may be dishonest, Byzantine agents. Decision problems with these features underlie applications such as reputation and recommendation systems in e-commerce, and resource location systems in peer-to-peer networks. Assuming the number of honest users is at least a constant fraction of the number of resources, and that the honest users can be partitioned into groups such that individuals in a group make identical assessments of resources, we present an algorithm whose expected regret per user is linear in the number of groups and only logarithmic in the number of resources. This bound compares favorably with the naïve approach in which each user ignores feedback from peers and chooses resources using a multi-armed bandit algorithm; in this case the expected regret per user would be polynomial in the number of resources.