Federated Learning (FL) enables collaborative model training without data sharing, yet participants face a fundamental challenge, e.g., simultaneously ensuring fairness across demographic groups while protecting sensitive client data. We introduce a differentially private fair FL algorithm (FedPF) that transforms this multi-objective optimization into a zero-sum game where fairness and privacy constraints compete against model utility. Our theoretical analysis reveals an inverse relationship: privacy mechanisms that protect sensitive attributes can reduce the statistical power available for detecting and correcting demographic biases under finite samples in federated settings. We further show that our theoretical bounds are consistent with a non-monotonic fairness-utility relationship, which is empirically validated by experiments where moderate fairness constraints improve generalization before excessive enforcement degrades performance. Compared with mainstream algorithms, even under strict privacy constraints, FedPF still maintains the lowest discrimination level among all tested algorithms while retaining high utility. Experimental validation demonstrates up to 42.9 % discrimination reduction across three datasets while maintaining competitive accuracy, but more importantly, reveals that achieving strong privacy and fairness simultaneously requires carefully balanced tradeoffs rather than optimizing either objective in isolation. Furthermore, hardware-level simulations demonstrate that FedPF maintains a low computational footprint, making it suitable for resource-constrained edge devices. The source code for our proposed algorithm is publicly accessible at https://github.com/szpsunkk/FedPF.

翻译：摘要：联邦学习（FL）无需共享数据即可实现协同模型训练，但参与者面临一个根本性挑战，例如在保护敏感客户端数据的同时，确保跨人口群体的公平性。我们提出了一种差分隐私公平联邦学习算法（FedPF），该算法将这一多目标优化问题转化为零和博弈，其中公平性与隐私约束相互竞争模型效用。我们的理论分析揭示了一种逆相关关系：保护敏感属性的隐私机制会降低联邦场景下有限样本中检测和纠正人口统计偏差的统计能力。我们进一步证明，理论边界与公平性-效用的非单调关系一致，实验验证了适度公平约束可提升泛化性能，而过度追求公平时性能则会下降。与主流算法相比，即使在严格隐私约束下，FedPF仍能在保持高效用的同时，在所有测试算法中维持最低歧视水平。实验验证表明，在三个数据集上，该算法在保持竞争性精度的同时，歧视程度降低高达42.9%；更关键的是，实证结果揭示，同时实现强隐私与强公平需要谨慎权衡，而非孤立优化任一目标。此外，硬件级仿真显示，FedPF保持较低计算开销，适用于资源受限的边缘设备。所提算法的源代码已公开于https://github.com/szpsunkk/FedPF。