Fairness in Streaming Submodular Maximization Subject to a Knapsack Constraint

Submodular optimization has been identified as a powerful tool for many data mining applications, where a representative subset of moderate size needs to be extracted from a large-scale dataset. In scenarios where data points possess sensitive attributes such as age, gender, or race, it becomes imperative to integrate fairness measures into submodular optimization to mitigate bias and discrimination. In this paper, we study the fundamental problem of fair submodular maximization subject to a knapsack constraint and propose the first streaming algorithm for it with provable performance guarantees for both monotone and non-monotone submodular functions. As a byproduct, we also propose a streaming algorithm for submodular maximization subject to a partition matroid and a knapsack constraint, significantly improving the performance bounds achieved by previous work. We conduct extensive experiments on real-world applications such as movie recommendation, image summarization, and maximum coverage in social networks. The experimental results strongly demonstrate the superiority of our proposed algorithms in terms of both fairness and utility.