Federated learning (FL) has garnered considerable attention due to its privacy-preserving feature. Nonetheless, the lack of freedom in managing user data can lead to group fairness issues, where models are biased towards sensitive factors such as race or gender. To tackle this issue, this paper proposes a novel algorithm, fair federated averaging with augmented Lagrangian method (FFALM), designed explicitly to address group fairness issues in FL. Specifically, we impose a fairness constraint on the training objective and solve the minimax reformulation of the constrained optimization problem. Then, we derive the theoretical upper bound for the convergence rate of FFALM. The effectiveness of FFALM in improving fairness is shown empirically on CelebA and UTKFace datasets in the presence of severe statistical heterogeneity.

翻译：联邦学习因其隐私保护特性而受到广泛关注。然而，用户数据管理缺乏自由可能导致群体公平性问题，即模型对种族或性别等敏感因素产生偏差。为解决这一问题，本文提出了一种新型算法——基于增广拉格朗日方法的公平联邦平均算法，该算法专门设计用于处理联邦学习中的群体公平性挑战。具体而言，我们在训练目标中施加公平性约束，并求解约束优化问题的极小极大重构形式。随后，我们推导了FFALM收敛速率的理论上界。在严重统计异质性条件下，基于CelebA和UTKFace数据集的实验结果表明，FFALM在提升公平性方面具有显著有效性。