Robust Budget Allocation Via Continuous Submodular Functions
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Author(s)
Staib, Matthew
Jegelka, Stefanie Sabrina
Date Issued
March 2019
Journal
Applied Mathematics & Optimization
Publisher
Springer Science and Business Media LLC
Citation
Staib, Matthew and Stefanie Jegelka. "Robust Budget Allocation Via Continuous Submodular Functions." Applied Mathematics & Optimization 82, 3 (March 2019): 1049–1079 © 2019 Springer Science Business Media, LLC, part of Springer Nature
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Author's final manuscript
Abstract
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. (in: WWW’12 - Proceedings of the 21st Annual Conference on World Wide, ACM, New York, 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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
https://doi.org/10.1007/s00245-019-09567-0
