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

## TL;DR

This paper introduces an exact method for maximizing the CVaR of stochastic submodular functions under constraints, providing a new approach for risk-averse optimization with practical applications.

## Contribution

It develops valid inequalities and an exact solution method for constrained CVaR maximization of stochastic submodular functions, assuming efficient CVaR oracle access.

## Key findings

- Effective solution method demonstrated on stochastic set covering problem.
- Valid inequalities improve computational efficiency.
- Method applicable to problems with efficient CVaR oracles.

## 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.