Optimization of Chance-Constrained Submodular Functions

TL;DR

This paper analyzes the effectiveness of greedy algorithms for optimizing submodular functions under chance constraints, demonstrating their strong performance with surrogate bounds and applications to social network problems.

Contribution

It provides the first analysis of greedy algorithms' approximation behavior for chance-constrained submodular optimization, highlighting their practical effectiveness.

Findings

Greedy algorithms perform well with Chernoff bound surrogates.

High-quality solutions are achievable under strict chance constraints.

Algorithms are effective in social network optimization problems.

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.