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

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…
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Taxonomy
TopicsDistributed Control Multi-Agent Systems · Mathematical and Theoretical Epidemiology and Ecology Models · Mathematical Biology Tumor Growth
