Ensure Differential Privacy and Convergence Accuracy in Consensus Tracking and Aggregative Games with Coupling Constraints

TL;DR

This paper introduces a novel distributed algorithm that ensures both differential privacy and convergence to the generalized Nash equilibrium in aggregative games with coupling constraints, supported by a new consensus-tracking method and convergence analysis.

Contribution

It presents the first GNE seeking algorithm that guarantees epsilon-differential privacy and convergence, along with a new consensus-tracking algorithm and a general convergence theorem for stochastic fixed-point iterations.

Findings

Algorithm achieves provable convergence and privacy guarantees.

Numerical simulations confirm effectiveness and privacy preservation.

New convergence analysis for stochastic nonstationary fixed-point processes.

Abstract

We address differential privacy for fully distributed aggregative games with shared coupling constraints. By co-designing the generalized Nash equilibrium (GNE) seeking mechanism and the differential-privacy noise injection mechanism, we propose the first GNE seeking algorithm that can ensure both provable convergence to the GNE and rigorous epsilon-differential privacy, even with the number of iterations tending to infinity. As a basis of the co-design, we also propose a new consensus-tracking algorithm that can achieve rigorous epsilon-differential privacy while maintaining accurate tracking performance, which, to our knowledge, has not been achieved before. To facilitate the convergence analysis, we also establish a general convergence result for stochastically-perturbed nonstationary fixed-point iteration processes, which lie at the core of numerous optimization and variational problems. Numerical simulation results confirm the effectiveness of the proposed approach.