From Noisy Fixed-Point Iterations to Private ADMM for Centralized and Federated Learning

TL;DR

This paper presents a unified framework for analyzing differentially private algorithms as noisy fixed-point iterations, leading to new private ADMM algorithms with strong privacy and utility guarantees for centralized, federated, and decentralized learning.

Contribution

It introduces a novel perspective on private optimization algorithms, enabling the design and analysis of new private ADMM methods within a flexible fixed-point iteration framework.

Findings

Recovered popular private gradient methods like DP-SGD.

Derived new private ADMM algorithms for various learning settings.

Established strong privacy and utility guarantees for these algorithms.

Abstract

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.