  Restless multi-armed bandits are often used to model budget-constrained
resource allocation tasks where receipt of the resource is associated with an
increased probability of a favorable state transition. Prior work assumes that
individual arms only benefit if they receive the resource directly. However,
many allocation tasks occur within communities and can be characterized by
positive externalities that allow arms to derive partial benefit when their
neighbor(s) receive the resource. We thus introduce networked restless bandits,
a novel multi-armed bandit setting in which arms are both restless and embedded
within a directed graph. We then present Greta, a graph-aware, Whittle
index-based heuristic algorithm that can be used to efficiently construct a
constrained reward-maximizing action vector at each timestep. Our empirical
results demonstrate that Greta outperforms comparison policies across a range
of hyperparameter values and graph topologies.
