Beyond Submodularity: A Unified Framework of Randomized Set Selection with Group Fairness Constraints

Abstract: Machine learning algorithms play an important role in a variety of important decision-making processes, including targeted advertisement displays, home loan approvals, and criminal behavior predictions. Given the far-reaching impact of these algorithms, it is crucial that they operate fairly, free from bias or prejudice towards certain groups in the population. Ensuring impartiality in these algorithms is essential for promoting equality and avoiding discrimination. To this end we introduce a unified framework for randomized subset selection that incorporates group fairness constraints. Our problem involves a global utility function and a set of group utility functions for each group, here a group refers to a group of individuals (e.g., people) sharing the same attributes (e.g., gender). Our aim is to generate a distribution across feasible subsets, specifying the selection probability of each feasible set, to maximize the global utility function while meeting a predetermined quota for each group utility function in expectation. Note that there may not necessarily be any direct connections between the global utility function and each group utility function. We demonstrate that this framework unifies and generalizes many significant applications in machine learning and operations research. Our algorithmic results either improves the best known result or provide the first approximation algorithms for new applications.