Distributed Nonconvex Optimization with Double Privacy Protection and Exact Convergence

TL;DR

This paper introduces a decentralized algorithm that provides strong privacy guarantees and guarantees convergence for nonconvex distributed optimization, improving privacy and efficiency over existing methods.

Contribution

The paper proposes a novel decentralized primal-dual algorithm with double privacy protection that ensures differential privacy and exact convergence in nonconvex settings.

Findings

Ensures differential privacy for local objectives.

Achieves sublinear convergence to a stationary point.

Attains linear convergence under P-{\

Abstract

Motivated by the pervasive lack of privacy protection in existing distributed nonconvex optimization methods, this paper proposes a decentralized proximal primal-dual algorithm enabling double protection of privacy ($\text{DPP}^2$) for minimizing nonconvex sum-utility functions over multi-agent networks, which ensures zero leakage of critical local information during inter-agent communications. We develop a two-tier privacy protection mechanism that first merges the primal and dual variables by means of a variable transformation, followed by embedding an additional random perturbation to further obfuscate the transmitted information. We theoretically establish that $\text{DPP}^2$ ensures differential privacy for local objectives while achieving exact convergence under nonconvex settings. Specifically, $\text{DPP}^2$ converges sublinearly to a stationary point and attains a linear convergence rate under the additional Polyak-{\L}ojasiewicz (P-{\L}) condition. Finally, a numerical example demonstrates the superiority of $\text{DPP}^2$ over a number of state-of-the-art algorithms, showcasing the faster, exact convergence achieved by $\text{DPP}^2$ under the same level of differential privacy.