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.

In this paper, we specifically investigate the deep equilibrium model (DEQ), an infinite-depth neural network with shared weight matrices across layers.

In this paper we adapt the nearest neighbour rule to the contextual bandit problem.

In this paper we adapt the nearest neighbour rule to the contextual bandit problem.

Such a perspective has been explored in Chen et al.[8], for instance, to build an equivalence between function approximation and graph isomorphism testing by GNNs. Forexample, consider FMPNN, the family of all Message Passing Neural Networks onG. Similar holds for the family of allk-Invariant Graph Functions (k-IGNs). Two k-typles, (ii,...,ik),(j1,...,jk) Vk are said to be in the same equivalent class if a permutation π on V such that (π(ii),...,π(ik)) = (j1,...,jk). Thus, both(10) and (11) can be proved analogously to how(11) is provedforcase2.