Federated Learning (FL) enables collaborative training on decentralized data. Differential privacy (DP) is crucial for FL, but current private methods often rely on unrealistic assumptions (e.g., bounded gradients or heterogeneity), hindering practical application. Existing works that relax these assumptions typically neglect practical FL features, including multiple local updates and partial client participation. We introduce Fed-$α$-NormEC, the first differentially private FL framework providing provable convergence and DP guarantees under standard assumptions while fully supporting these practical features. Fed-$α$-NormE integrates local updates (full and incremental gradient steps), separate server and client stepsizes, and, crucially, partial client participation, which is essential for real-world deployment and vital for privacy amplification. Our theoretical guarantees are corroborated by experiments on private deep learning tasks.

翻译：联邦学习（FL）支持在分散数据上进行协同训练。差分隐私（DP）对FL至关重要，但现有私有方法通常依赖于不切实际的假设（例如梯度有界性或数据异质性），阻碍了实际应用。现有放宽这些假设的研究往往忽略了实际FL的关键特性，包括多轮本地更新和部分客户端参与。我们提出了Fed-$α$-NormEC，这是首个在标准假设下提供可证明收敛性与DP保证的差分隐私FL框架，同时完整支持上述实际特性。Fed-$α$-NormE整合了本地更新（完整与增量梯度步长）、独立的服务器与客户端步长，以及至关重要的部分客户端参与机制——这对实际部署不可或缺且能有效增强隐私保护。我们通过私有深度学习任务的实验验证了理论保证的有效性。