Differentially Private Decentralized Weakly Convex Delay-Tolerance Optimization in Robust Phase Retrieval

This paper studies a particular facet of the Decentralized Robust Phase Retrieval (DRPR) problem under random time-delay interference. The problem setting encompasses a network of agents, each possessing exclusive access to a localized weakly convex (WC) objective function, and engaging in communication with their neighboring entities under delays. In addressing this intricate issue, we put forth a novel differential privacy distributed Weakly Convex Optimization (WCO) algorithm, termed as DP-DWDTA. We validate the convergence of the DP-DWDTA by employing diminishing step-sizes and assessing it through Moreau Envelope (ME) measurement. Furthermore, we establish the privacy of the DP-DWDTA by introducing differential privacy through the addition of Laplacian noise. Finally, the empirical results procured from an array of DRPR experiments featuring four distinct images subject to noise substantiate the efficiency of the DP-DWDTA. These findings reinforce DP-DWDTA's capabilities in adeptly addressing privacy preservation in DRPR circumstances under time delay interference.