Distributed Double Accelerated Algorithm for Differentially Private Optimization

doi:10.1109/tcns.2026.3691792

Distributed Double Accelerated Algorithm for Differentially Private Optimization

2026-05-12

0

PRE

AI

DOI：10.1109/tcns.2026.3691792

Original

Original request for help

Save

Abstract

En 中文

In differentially private distributed optimization, some studies mainly utilize diminishing stepsize or interaction weakening to gradually reduce sensitivity to improve the tradeoff between privacy and optimality. However, these approaches often come at the expense of the convergence rate. Commonly used acceleration methods, such as Nesterov gradient method and heavy-ball method, contribute to the fast convergence, but their dependence on historical information poses challenge to the privacy analysis in accelerated differentially private algorithms. To address this, a differentially private distributed optimization algorithm is proposed, named as the differentially private algorithm based on the gradient tracking and double accelerated (DP-GTDA) method, where double means that both distributed heavy-ball and distributed Nesterov gradient methods are introduced to accelerate convergence. Leveraging spectral radius analysis of a 4-D matrix and tail probability estimation, the accelerated linear convergence to optimal solution is established in mean and almost surely. Due to the careful design in information aggregation step, the privacy level of DP-GTDA can be determined based on differential privacy over a finite time horizon. Simulations are conducted on a distributed sensing problem to verify theoretical findings.

Keywords:

Acceleration

differential privacy

distributed optimization

linear convergence

Distributed Double Accelerated Algorithm for Differentially Private Optimization

Abstract

Journal

Organization

Cited Papers