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.

翻译：近期联邦学习（FL）的进展使得大规模且广泛分布的客户端能够协作训练机器学习（ML）模型，同时保护其隐私。然而，当不同客户端的数据集存在异质性时，传统FL机制生成的全局模型无法充分代表数据资源有限的弱势客户端，导致其局部数据上的准确率较低且偏差较高。根据描述优势方随时间获得更多优势、劣势方失去更多优势的马太效应，将此类全局模型部署至客户端应用程序中可能加剧客户端间的资源差异，并损害社会福利与公平性原则。为缓解马太效应，我们提出平等公平联邦学习（EFFL），其中平等公平性指从FL中学习到的全局模型需满足：（1）各客户端间准确率相等；（2）各客户端间决策偏差相等。除实现客户端间的平等公平性外，EFFL还追求性能最优性，即最小化每个客户端的经验风险损失与偏差——这无论对集中式还是分布式ML模型训练均至关重要。我们将EFFL建模为带约束的多约束多目标优化（MCMOO）问题，以决策偏差和平等公平性为约束，以最小化所有客户端的经验风险损失作为待优化的多个目标，提出基于梯度的三阶段算法以获取约束空间内的帕累托最优解。大量实验表明，在实现高性能全局模型并增强所有客户端间平等公平性方面，EFFL优于其他最先进的FL算法。