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）机器学习算法作为含噪不动点迭代的实例进行研究，旨在从这一经过充分研究的框架中推导出隐私与效用结果。我们表明，这一新视角不仅能复现流行的基于梯度的私有方法（如DP-SGD），还能以灵活的方式为设计和分析新型私有优化算法提供原理性指导。聚焦于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、联邦式和完全分布式学习推导出新颖的私有ADMM算法。针对这三种算法，我们通过利用迭代和子采样造成的隐私放大效应，建立了强隐私保证。最后，我们借助最近针对含噪不动点迭代的线性收敛结果，采用统一分析给出了效用保证。