Maximizing Non-Monotone DR-Submodular Functions with Cardinality Constraints

TL;DR

This paper introduces the first polynomial-time algorithms for maximizing non-monotone DR-submodular functions under a cardinality constraint, with applications demonstrated on revenue maximization.

Contribution

It presents novel approximation algorithms for non-monotone DR-submodular maximization with cardinality constraints, advancing optimization techniques in machine learning and combinatorial problems.

Findings

Algorithms achieve near-optimal solutions within polynomial time

Experimental results show effective performance on real-world revenue data

First polynomial-time solutions for this class of problems

Abstract

We consider the problem of maximizing a non-monotone DR-submodular function subject to a cardinality constraint. Diminishing returns (DR) submodularity is a generalization of the diminishing returns property for functions defined over the integer lattice. This generalization can be used to solve many machine learning or combinatorial optimization problems such as optimal budget allocation, revenue maximization, etc. In this work we propose the first polynomial-time approximation algorithms for non-monotone constrained maximization. We implement our algorithms for a revenue maximization problem with a real-world dataset to check their efficiency and performance.