We study differentially private (DP) machine learning algorithms as instances of noisy fixed-point iterations, in order to derive privacy and utility results from this well-studied framework. We show that this new perspective recovers popular private gradient-based methods like DP-SGD and provides a principled way to design and analyze new private optimization algorithms in a flexible manner. Focusing on the widely-used Alternating Directions Method of Multipliers (ADMM) method, we use our general framework to derive novel private ADMM algorithms for centralized, federated and fully decentralized learning. For these three algorithms, we establish strong privacy guarantees leveraging privacy amplification by iteration and by subsampling. Finally, we provide utility guarantees using a unified analysis that exploits a recent linear convergence result for noisy fixed-point iterations.

翻译：我们把差分隐私（DP）机器学习算法视为带噪不动点迭代的实例，以便从这个经过充分研究的框架中推导隐私与效用结果。我们表明，这一新视角能重新导出流行的基于梯度的私有方法（如DP-SGD），并以灵活的方式为设计和分析新的私有优化算法提供原则性途径。聚焦于广泛使用的交替方向乘子法（ADMM），我们利用通用框架推导出适用于集中式、联邦式及完全分散式学习的全新私有ADMM算法。针对这三种算法，我们借助迭代随机化和子采样带来的隐私放大效应，建立了强有力的隐私保证。最后，我们利用近期关于带噪不动点迭代线性收敛性的统一分析结果，给出了效用保证。