  We consider an online influence maximization problem in which a decision
maker selects a node among a large number of possibilities and places a piece
of information at the node. The node transmits the information to some others
that are in the same connected component in a random graph. The goal of the
decision maker is to reach as many nodes as possible, with the added
complication that feedback is only available about the degree of the selected
node. Our main result shows that such local observations can be sufficient for
maximizing global influence in two broadly studied families of random graph
models: stochastic block models and Chung--Lu models. With this insight, we
propose a bandit algorithm that aims at maximizing local (and thus global)
influence, and provide its theoretical analysis in both the subcritical and
supercritical regimes of both considered models. Notably, our performance
guarantees show no explicit dependence on the total number of nodes in the
network, making our approach well-suited for large-scale applications.
