Abstract
We consider fairness in submodular maximization subject to a knapsack constraint, a fundamental problem with various applications in economics, machine learning, and data mining. In the model, we are given a set of ground elements, each associated with a weight and a color, and a monotone submodular function defined over them. The goal is to maximize the submodular function while guaranteeing that the total weight does not exceed a specified budget (the knapsack constraint) and that the number of elements selected for each color falls within a designated range (the fairness constraint).
While there exists some recent literature on this topic, the existence of a non-trivial approximation for the problem -- without relaxing either the knapsack or fairness constraints -- remains a challenging open question. This paper makes progress in this direction. We demonstrate that when the number of colors is constant, there exists a polynomial-time algorithm that achieves a constant approximation with high probability. Additionally, we show that if either the knapsack or fairness constraint is relaxed only to require expected satisfaction, a tight approximation ratio of $(1-1/e-\epsilon)$ can be obtained in expectation for any $\epsilon >0$.
While there exists some recent literature on this topic, the existence of a non-trivial approximation for the problem -- without relaxing either the knapsack or fairness constraints -- remains a challenging open question. This paper makes progress in this direction. We demonstrate that when the number of colors is constant, there exists a polynomial-time algorithm that achieves a constant approximation with high probability. Additionally, we show that if either the knapsack or fairness constraint is relaxed only to require expected satisfaction, a tight approximation ratio of $(1-1/e-\epsilon)$ can be obtained in expectation for any $\epsilon >0$.
Original language | English |
---|---|
Title of host publication | 34th International Joint Conference on Artificial Intelligence (IJCAI 2025) |
Publication status | Accepted/In press/Filed - 29 Apr 2025 |
Event | 34th International Joint Conference on Artificial Intelligence (2025) - Montreal, Canada Duration: 16 Aug 2025 → 22 Aug 2025 https://2025.ijcai.org/ |
Conference
Conference | 34th International Joint Conference on Artificial Intelligence (2025) |
---|---|
Abbreviated title | IJCAI 2025 |
Country/Territory | Canada |
City | Montreal |
Period | 16/08/25 → 22/08/25 |
Internet address |