Optimization of Chance-Constrained Submodular Functions

  • Benjamin Doerr cole Polytechnique
  • Carola Doerr Sorbonne University
  • Aneta Neumann The University of Adelaide
  • Frank Neumann The University of Adelaide
  • Andrew Sutton University of Minnesota

Abstract

Submodular optimization plays a key role in many real-world problems. In many real-world scenarios, it is also necessary to handle uncertainty, and potentially disruptive events that violate constraints in stochastic settings need to be avoided. In this paper, we investigate submodular optimization problems with chance constraints. We provide a first analysis on the approximation behavior of popular greedy algorithms for submodular problems with chance constraints. Our results show that these algorithms are highly effective when using surrogate functions that estimate constraint violations based on Chernoff bounds. Furthermore, we investigate the behavior of the algorithms on popular social network problems and show that high quality solutions can still be obtained even if there are strong restrictions imposed by the chance constraint.

Published
2020-04-03
Section
AAAI Technical Track: Constraint Satisfaction and Optimization