Maximizing Non-Monotone DR-Submodular Functions with Cardinality Constraints
This addresses optimization challenges in machine learning and combinatorial problems like budget allocation, though it appears incremental as it builds on existing submodular function theory.
The paper tackled the problem of maximizing non-mononotone DR-submodular functions under cardinality constraints, proposing the first polynomial-time approximation algorithms and demonstrating their efficiency with real-world revenue maximization data.
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.