The issue of group fairness in machine learning models, where certain sub-populations or groups are favored over others, has been recognized for some time. While many mitigation strategies have been proposed in centralized learning, many of these methods are not directly applicable in federated learning, where data is privately stored on multiple clients. To address this, many proposals try to mitigate bias at the level of clients before aggregation, which we call locally fair training. However, the effectiveness of these approaches is not well understood. In this work, we investigate the theoretical foundation of locally fair training by studying the relationship between global model fairness and local model fairness. Additionally, we prove that for a broad class of fairness metrics, the global model's fairness can be obtained using only summary statistics from local clients. Based on that, we propose a globally fair training algorithm that directly minimizes the penalized empirical loss. Real-data experiments demonstrate the promising performance of our proposed approach for enhancing fairness while retaining high accuracy compared to locally fair training methods.

翻译：机器学习模型中的群体公平性问题，即某些子群体或群体受到偏袒，已受到关注一段时间。尽管在集中式学习中已提出许多缓解策略，但这些方法大多无法直接适用于数据分布在多个客户端上私有存储的联邦学习。为此，许多方案试图在聚合前在客户端层面缓解偏差，我们称之为局部公平训练。然而，这些方法的有效性尚不明确。在本研究中，我们通过探索全局模型公平性与局部模型公平性之间的关系，深入研究了局部公平训练的理论基础。此外，我们证明对于一大类公平性指标，仅利用来自局部客户端的汇总统计量即可获得全局模型的公平性。基于此，我们提出了一种直接最小化惩罚经验损失的全局公平训练算法。真实数据实验表明，与局部公平训练方法相比，我们提出的方法在保持高准确率的同时，能有效提升公平性。