Optimizing Chance-Constrained Submodular Problems with Variable Uncertainties
This addresses optimization problems with stochastic constraints for applications like resource allocation and network influence, but it is incremental as it extends prior work on fixed uncertainties to variable ones.
The paper tackles chance-constrained submodular optimization problems with variable uncertainties in item weights, providing the first rigorous analysis for this setting and presenting greedy algorithms that achieve a constant approximation ratio, with effective performance demonstrated on maximum coverage and influence maximization instances.
Chance constraints are frequently used to limit the probability of constraint violations in real-world optimization problems where the constraints involve stochastic components. We study chance-constrained submodular optimization problems, which capture a wide range of optimization problems with stochastic constraints. Previous studies considered submodular problems with stochastic knapsack constraints in the case where uncertainties are the same for each item that can be selected. However, uncertainty levels are usually variable with respect to the different stochastic components in real-world scenarios, and rigorous analysis for this setting is missing in the context of submodular optimization. This paper provides the first such analysis for this case, where the weights of items have the same expectation but different dispersion. We present greedy algorithms that can obtain a high-quality solution, i.e., a constant approximation ratio to the given optimal solution from the deterministic setting. In the experiments, we demonstrate that the algorithms perform effectively on several chance-constrained instances of the maximum coverage problem and the influence maximization problem.