Fairness k-Submodular Maximization Subject to Matroid Constraint

Abstract

Fairness k-submodular maximization has attracted increasing interest due to its broad relevance in artificial intelligence and machine learning. However, most existing works are limited to monotone objectives or simple size constraints, while non-monotone settings with richer constraints remain largely unexplored. In this paper, we first introduce a constant-factor approximation algorithm for the problem with a general non-monotone objective function under a matroid constraint. Our approach is built upon a two-stage algorithmic framework. Specifically, we first develop an algorithm that guarantees feasibility with respect to upper fairness bounds only. We then show how this algorithm can be systematically extended to simultaneously enforce fairness bounds, while preserving provable approximation guarantees. Comprehensive experiments on standard benchmark datasets demonstrate that our algorithm achieves competitive objective values while maintaining a favorable balance between fairness guarantees and query complexity efficiency compared to existing state-of-the-art methods.