  The optimal allocation of resources for maximizing influence, spread of
information or coverage, has gained attention in the past years, in particular
in machine learning and data mining. But in applications, the parameters of the
problem are rarely known exactly, and using wrong parameters can lead to
undesirable outcomes. We hence revisit a continuous version of the Budget
Allocation or Bipartite Influence Maximization problem introduced by Alon et
al. (2012) from a robust optimization perspective, where an adversary may
choose the least favorable parameters within a confidence set. The resulting
problem is a nonconvex-concave saddle point problem (or game). We show that
this nonconvex problem can be solved exactly by leveraging connections to
continuous submodular functions, and by solving a constrained submodular
minimization problem. Although constrained submodular minimization is hard in
general, here, we establish conditions under which such a problem can be solved
to arbitrary precision $\epsilon$.
