Distributed Gradient Tracking for Differentially Private Multi-Agent Optimization With a Dynamic Event-Triggered Mechanism

Distributed optimization achieves a minimized objective function through collaboration among distributed agents. Considering limited communication capabilities and privacy concerns, this article proposes a dynamic event-triggered differentially private gradient-tracking algorithm for distributed optimization. The communication requirement is reduced by event triggering, while the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon$</tex-math> </inline-formula> -differential privacy is guaranteed by perturbations on states and the tracking of the average gradient. The convergence point is uniquely determined by the noise injected to the tracking. Sufficient conditions for stepsizes are established theoretically to guarantee the convergence in mean and almost surely. Moreover, the theoretical privacy level is rigorously obtained and the positive effect of the event-triggered communication on the privacy is also discussed. Simulations are conducted for the classification of the dataset on the stability of a 4-node star power system to verify the theoretical findings.