Communication-Efficient Differentially Private Gradient Tracking for Distributed Optimization via Local Updates
Abstract
This paper studies privacy-preserving distributed optimization using gradient tracking with one communication-free local update between consecutive communication rounds. Since local computation alone does not protect gradient information, we perturb both the primal state and the gradient-tracking direction at communication iterations while keeping local updates noise-free. We establish an aggregate variable for tracking, characterize the limiting consensus point in the presence of added random noise, and prove convergence in mean under certain parameter conditions. We also establish infinite-horizon pure differential privacy for the complete communication transcript under an affine objective adjacency relation and geometrically decaying Laplace perturbations. Simulation results illustrate the advantages of the proposed method in terms of the convergence and optimization accuracy given a privacy budget.
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BibTeX
@misc{maithripala2026communicationefficient,
title = {{Communication-Efficient Differentially Private Gradient Tracking for Distributed Optimization via Local Updates}},
author = {Mihitha Maithripala and Chenyang Qiu and Zongli Lin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04854},
eprint = {2610.04854},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04854},
}
RIS
TY - UNPB
TI - Communication-Efficient Differentially Private Gradient Tracking for Distributed Optimization via Local Updates
AU - Mihitha Maithripala
AU - Chenyang Qiu
AU - Zongli Lin
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.04854
UR - https://arxiv.org/abs/2610.04854
AB - This paper studies privacy-preserving distributed optimization using gradient tracking with one communication-free local update between consecutive communication rounds. Since local computation alone does not protect gradient information, we perturb both the primal state and the gradient-tracking direction at communication iterations while keeping local updates noise-free. We establish an aggregate variable for tracking, characterize the limiting consensus point in the presence of added random noise, and prove convergence in mean under certain parameter conditions. We also establish infinite-horizon pure differential privacy for the complete communication transcript under an affine objective adjacency relation and geometrically decaying Laplace perturbations. Simulation results illustrate the advantages of the proposed method in terms of the convergence and optimization accuracy given a privacy budget.
ER -