Enhancing Accuracy in Differentially Private Distributed Optimization Through Sensitivity Reduction

TL;DR

This paper introduces a new differentially private distributed optimization algorithm that reduces sensitivity to improve accuracy, provides explicit noise parameter formulas, and proves strong privacy and convergence guarantees.

Contribution

It presents a novel sensitivity-reduction technique for distributed algorithms, enabling higher accuracy under differential privacy constraints.

Findings

Achieves arbitrarily rigorous $$-differential privacy.

Proves convergence in the mean square sense.

Provides an upper bound on optimization accuracy.

Abstract

In this paper, we investigate the problem of differentially private distributed optimization. Recognizing that lower sensitivity leads to higher accuracy, we analyze the key factors influencing the sensitivity of differentially private distributed algorithms. Building on these insights, we propose a novel differentially private distributed algorithm for undirected graphs that enhances optimization accuracy by reducing sensitivity. To ensure practical applicability, we derive an explicit closed-form expression for the noise parameter as a function of the privacy budget. Moreover, we rigorously prove that the proposed algorithm can achieve arbitrarily rigorous $\epsilon$-differential privacy, establish its convergence in the mean square sense, and provide an upper bound on its optimization accuracy. Finally, extensive comparisons with various privacy-preserving methods validate the effectiveness of our algorithm.