A Weighted Gradient Tracking Privacy-Preserving Method for Distributed Optimization
This addresses privacy risks for agents in distributed optimization systems, representing an incremental improvement over existing gradient tracking methods.
The paper tackles privacy leakage in distributed optimization with gradient tracking by proposing a weighted gradient tracking method with decaying weight factors, proving convergence to the optimal solution and validating effectiveness through numerical simulations on distributed estimation and CNN training.
This paper investigates the privacy-preserving distributed optimization problem, aiming to protect agents' private information from potential attackers during the optimization process. Gradient tracking, an advanced technique for improving the convergence rate in distributed optimization, has been applied to most first-order algorithms in recent years. We first reveal the inherent privacy leakage risk associated with gradient tracking. Building upon this insight, we propose a weighted gradient tracking distributed privacy-preserving algorithm, eliminating the privacy leakage risk in gradient tracking using decaying weight factors. Then, we characterize the convergence of the proposed algorithm under time-varying heterogeneous step sizes. We prove the proposed algorithm converges precisely to the optimal solution under mild assumptions. Finally, numerical simulations validate the algorithm's effectiveness through a classical distributed estimation problem and the distributed training of a convolutional neural network.