A Gang of Adversarial Bandits Mark Herbster*, Stephen Pasteris* Fabio Vitale Department of Computer Science University of Lille University College London 59653 Villeneuve d'Ascq CEDEX London WC1E 6BT

We consider running multiple instances of multi-armed bandit (MAB) problems in parallel. A main motivation for this study are online recommendation systems, in which each of N users is associated with a MAB problem and the goal is to exploit users' similarity in order to learn users' preferences to K items more efficiently. We consider the adversarial MAB setting, whereby an adversary is free to choose which user and which loss to present to the learner during the learning process. Users are in a social network and the learner is aided by a-priori knowledge of the strengths of the social links between all pairs of users. It is assumed that if the social link between two users is strong then they tend to share the same action. The regret is measured relative to an arbitrary function which maps users to actions. The smoothness of the function is captured by a resistance-based dispersion measure Ψ.