Ensuring fairness of machine learning (ML) algorithms is becoming an increasingly important mission for ML service providers. This is even more critical and challenging in the federated learning (FL) scenario, given a large number of diverse participating clients. Simply mandating equality across clients could lead to many undesirable consequences, potentially discouraging high-performing clients and resulting in sub-optimal overall performance. In order to achieve better equity rather than equality, in this work, we introduce and study proportional fairness (PF) in FL, which has a deep connection with game theory. By viewing FL from a cooperative game perspective, where the players (clients) collaboratively learn a good model, we formulate PF as Nash bargaining solutions. Based on this concept, we propose PropFair, a novel and easy-to-implement algorithm for effectively finding PF solutions, and we prove its convergence properties. We illustrate through experiments that PropFair consistently improves the worst-case and the overall performances simultaneously over state-of-the-art fair FL algorithms for a wide array of vision and language datasets, thus achieving better equity.
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