Matroids, Matchings, and Fairness

The need for fairness in machine learning algorithms is increasingly critical. A recent focus has been on developing fair versions of classical algorithms, such as those for bandit learning, regression, and clustering. In this work we extend this line of work to include algorithms for optimization subject to one or multiple matroid constraints. We map out a series of results, showing optimal solutions, approximation algorithms, and hardness proofs depending on the specific flavor of the problem. Our algorithms are efficient and empirical experiments demonstrate that fairness can be achieved with a modest compromise to the overall objective value.