Robust Budget Allocation via Continuous Submodular Functions
This addresses robust resource allocation for influence maximization in machine learning, but is incremental as it builds on prior work with a robust optimization perspective.
The paper tackles the robust budget allocation problem under uncertainty in parameters by formulating it as a nonconvex-concave saddle point problem, and shows it can be solved exactly using continuous submodular functions with arbitrary precision ε.
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 $ε$.