Nash equilibrium of multi-agent graphical game with a privacy information encrypted learning algorithm

TL;DR

This paper introduces a privacy-preserving decentralized learning algorithm for multi-agent graphical games, ensuring convergence to Nash equilibrium even under packet loss attacks and unreliable networks.

Contribution

It develops a secure hierarchical structure with an encryption scheme integrated into the learning process, addressing privacy and robustness in multi-agent systems.

Findings

Guaranteed convergence of the decentralized learning algorithm.

Successful embedding of encryption in data transmission.

Effective handling of packet loss attacks in simulations.

Abstract

This paper studies the global Nash equilibrium problem of leader-follower multi-agent dynamics, which yields consensus with a privacy information encrypted learning algorithm. With the secure hierarchical structure, the relationship between the secure consensus problem and global Nash equilibrium is discussed under potential packet loss attacks, and the necessary and sufficient condition for the existence of global Nash equilibrium is provided regarding the soft-constrained graphical game. To achieve the optimal policies, the convergence of decentralized learning algorithm is guaranteed with an iteratively updated pair of decoupled gains. By using the developed quantization scheme and additive-multiplicative property, the encryption-decryption is successfully embedded in the data transmission and computation to overcome the potential privacy violation in unreliable networks. A simulation example is provided to verify the effectiveness of the designed algorithm.