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：我们将差分隐私(DP)机器学习算法视为含噪不动点迭代的实例，以从这一成熟框架中推导隐私和效用结果。我们表明，这一新视角能够恢复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方法。聚焦广泛使用的交替方向乘子法(ADMM)，我们利用通用框架为集中式、联邦式和完全分散式学习推导出新颖的私有ADMM算法。针对这三种算法，我们通过迭代隐私放大和子采样隐私放大技术建立了强大的隐私保证。最后，我们利用含噪不动点迭代的最新线性收敛结果，通过统一分析提供了效用保证。