The core message of this paper is to provide a complete computational complexity map of the Robust Submodular Minimizer problem, which aims to find a set that is close to some optimal solution for each of the k given submodular functions, under a given recovery bound d.
Efficient algorithms are proposed for maximizing submodular objectives under noisy access to the objective function, achieving approximation guarantees close to the best possible in the standard value oracle setting.
The core message of this work is to introduce a novel formulation for multi-task submodular optimization that achieves local distributional robustness within the neighborhood of a reference distribution, which assigns importance scores to each task.