Statistical Privacy-Preserving Online Distributed Nash Equilibrium Tracking in Aggregative Games

• Published in: IEEE transactions on automatic control Vol. 69; no. 1; pp. 323 - 330
• Main Authors: Lin, Yeming, Liu, Kun, Han, Dongyu, Xia, Yuanqing
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Aggregates; Aggregative game; Algorithms; Cost function; distributed online algorithm; Game theory; Nash equilibrium; Perturbation methods; Players; Privacy; privacy preservation; Tracking
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2023.3264164

This article considers an online aggregative game equilibrium problem subject to privacy preservation, where all players aim at tracking the time-varying Nash equilibrium, while some players are corrupted by an adversary. We propose a distributed online Nash equilibrium tracking algorithm, where a correlated perturbation mechanism is employed to mask the local information of the players. Our theoretical analysis shows that the proposed algorithm can achieve a sublinear expected regret bound while preserving the privacy of uncorrupted players. We use the Kullback-Leibler divergence to analyze the privacy bound in a statistical sense. Furthermore, we present a tradeoff between the expected regret and the statistical privacy, to obtain a constant privacy bound when the regret bound is sublinear.