Improving the Privacy and Accuracy of ADMM-Based Distributed Algorithms

TL;DR

This paper introduces a correlated perturbation method for ADMM that enhances both privacy and utility in distributed machine learning, addressing limitations of previous differential privacy approaches over multiple iterations.

Contribution

It proposes a novel perturbation technique correlated with penalty parameters and a modified ADMM with adaptive penalty selection, improving privacy-utility tradeoff.

Findings

Improved privacy guarantees over multiple iterations.

Enhanced utility compared to previous differential privacy methods.

Convergence conditions and rate bounds for the modified ADMM.

Abstract

Alternating direction method of multiplier (ADMM) is a popular method used to design distributed versions of a machine learning algorithm, whereby local computations are performed on local data with the output exchanged among neighbors in an iterative fashion. During this iterative process the leakage of data privacy arises. A differentially private ADMM was proposed in prior work (Zhang & Zhu, 2017) where only the privacy loss of a single node during one iteration was bounded, a method that makes it difficult to balance the tradeoff between the utility attained through distributed computation and privacy guarantees when considering the total privacy loss of all nodes over the entire iterative process. We propose a perturbation method for ADMM where the perturbed term is correlated with the penalty parameters; this is shown to improve the utility and privacy simultaneously. The method is based on a modified ADMM where each node independently determines its own penalty parameter in every iteration and decouples it from the dual updating step size. The condition for convergence of the modified ADMM and the lower bound on the convergence rate are also derived.