  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.
