  Recent advances in federated learning (FL) enable collaborative training of
machine learning (ML) models from large-scale and widely dispersed clients
while protecting their privacy. However, when different clients' datasets are
heterogeneous, traditional FL mechanisms produce a global model that does not
adequately represent the poorer clients with limited data resources, resulting
in lower accuracy and higher bias on their local data. According to the Matthew
effect, which describes how the advantaged gain more advantage and the
disadvantaged lose more over time, deploying such a global model in client
applications may worsen the resource disparity among the clients and harm the
principles of social welfare and fairness. To mitigate the Matthew effect, we
propose Egalitarian Fairness Federated Learning (EFFL), where egalitarian
fairness refers to the global model learned from FL has: (1) equal accuracy
among clients; (2) equal decision bias among clients. Besides achieving
egalitarian fairness among the clients, EFFL also aims for performance
optimality, minimizing the empirical risk loss and the bias for each client;
both are essential for any ML model training, whether centralized or
decentralized. We formulate EFFL as a constrained multi-constrained
multi-objectives optimization (MCMOO) problem, with the decision bias and
egalitarian fairness as constraints and the minimization of the empirical risk
losses on all clients as multiple objectives to be optimized. We propose a
gradient-based three-stage algorithm to obtain the Pareto optimal solutions
within the constraint space. Extensive experiments demonstrate that EFFL
outperforms other state-of-the-art FL algorithms in achieving a
high-performance global model with enhanced egalitarian fairness among all
clients.
