An Exact Method for Constrained Maximization of the Conditional Value-at-Risk of a Class of Stochastic Submodular Functions

Abstract

We consider a class of risk-averse submodular maximization problems (RASM) where the objective is the conditional value-at-risk (CVaR) of a random nondecreasing submodular function at a given risk level. We propose valid inequalities and an exact general method for solving RASM under the assumption that we have an efficient oracle that computes the CVaR of the random function. We demonstrate the proposed method on a stochastic set covering problem that admits an efficient CVaR oracle for the random coverage function.

References in corpus (4)

• Maximizing Influence in Social Networks: A Two-Stage Stochastic Programming Approach That Exploits Submodularity
• Online Continuous Submodular Maximization
• Chance-Constrained Combinatorial Optimization with a Probability Oracle and Its Application to Probabilistic Partial Set Covering
• An Approximation Algorithm for Risk-averse Submodular Optimization