  We consider a ubiquitous scenario in the study of Influence Maximization
(IM), in which there is limited knowledge about the topology of the diffusion
network. We set the IM problem in a multi-round diffusion campaign, aiming to
maximize the number of distinct users that are influenced. Leveraging the
capability of bandit algorithms to effectively balance the objectives of
exploration and exploitation, as well as the expressivity of neural networks,
our study explores the application of neural bandit algorithms to the IM
problem. We propose the framework IM-GNB (Influence Maximization with Graph
Neural Bandits), where we provide an estimate of the users' probabilities of
being influenced by influencers (also known as diffusion seeds). This initial
estimate forms the basis for constructing both an exploitation graph and an
exploration one. Subsequently, IM-GNB handles the exploration-exploitation
tradeoff, by selecting seed nodes in real-time using Graph Convolutional
Networks (GCN), in which the pre-estimated graphs are employed to refine the
influencers' estimated rewards in each contextual setting. Through extensive
experiments on two large real-world datasets, we demonstrate the effectiveness
of IM-GNB compared with other baseline methods, significantly improving the
spread outcome of such diffusion campaigns, when the underlying network is
unknown.
