Fairness in Monotone k-submodular Maximization: Algorithms and Applications

Submodular optimization has become increasingly prominent in machine learning, and fairness has drawn much attention. In this paper, we propose to study the fair k-submodular maximization problem and develop a 1/3-approximation greedy algorithm with a running time of O(knB). Our theoretical guarantee matches the best-known k-submodular maximization results without fairness constraints. In addition, we have developed a faster threshold-based algorithm that achieves a (1/3 ϵ) approximation with ${\mathcal{O}}\left({\frac{{kn}}{\varepsilon }\log \frac{B}{\varepsilon }}\right)$ evaluations of the function−f. Furthermore, for both algorithms, we provide approximation guarantees when the k-submodular function is not accessible but only can be approximately accessed. We have extensively validated our theoretical findings through empirical study and examined the practical implications of fairness. The experimental results show that the fairness constraints do not significantly undermine the quality of solutions.