High Probability Guarantees for Submodular Maximization via Boosted Stochastic Greedy

Andrés C. Castillo J., Ege C. Kaya, Abolfazl Hashemi

Abstract: Submodular functions occur naturally in a wide range of areas and problems such as sensor selection, economics and algorithmic game theory. The Stochastic Greedy algorithm is a well-known method used in the efficient maximization of such functions in the presence of a cardinality constraint. In this paper, we study the shortcomings of Stochastic Greedy by demonstrating that in certain scenarios, the algorithm consistently achieves its worst-case approximation. We propose our own algorithm, Boosted Stochastic Greedy, which is robust against such scenarios and is shown to have strong theoretical guarantees as we demonstrate that our algorithm can ensure an approximation guarantee that holds with high probability.