A Gang of Bandits

Multi-armed bandit problems are receiving a great deal of attention because they adequately formalize the exploration-exploitation trade-offs arising in several industrially relevant applications, such as online advertisement and, more generally, recommendation systems. In many cases, however, these applications have a strong social component, whose integration in the bandit algorithm could lead to a dramatic performance increase. For instance, we may want to serve content to a group of users by taking advantage of an underlying network of social relationships among them. In this paper, we introduce novel algorithmic approaches to the solution of such networked bandit problems. More specifically, we design and analyze a global strategy which allocates a bandit algorithm to each network node (user) and allows it to "share" signals (contexts and payoffs) with the neghboring nodes. We then derive two more scalable variants of this strategy based on different ways of clustering the graph nodes. We experimentally compare the algorithm and its variants to state-of-the-art methods for contextual bandits that do not use the relational information. Our experiments, carried out on synthetic and real-world datasets, show a marked increase in prediction performance obtained by exploiting the network structure.