Optimization of Chance-Constrained Submodular Functions
This addresses uncertainty handling in real-world submodular problems like social networks, but it is incremental as it builds on existing greedy methods with new constraint analysis.
The paper tackles submodular optimization with chance constraints by analyzing greedy algorithms, showing they are highly effective when using Chernoff-bound-based surrogate functions and achieve high-quality solutions in social network problems despite strict constraints.
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.