  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.
