Decentralized online stochastic generalized Nash Equilibrium seeking for multi-cluster games: A Byzantine-resilient algorithm

TL;DR

This paper introduces a Byzantine-resilient decentralized algorithm for online stochastic generalized Nash equilibrium seeking in multi-cluster games, effectively mitigating malicious agents' influence and ensuring sublinear growth of regret and constraint violation.

Contribution

It develops a novel Byzantine-resilient algorithm combining variance reduction, dynamic consensus, and robust aggregation for online stochastic games with no prior Byzantine agent knowledge.

Findings

Resilient metrics grow sublinearly over time in expectation.

The algorithm effectively mitigates Byzantine agents' influence.

Numerical simulations validate theoretical results.

Abstract

This paper addresses the challenge of solving the generalized Nash Equilibrium seeking problem for decentralized stochastic online multi-cluster games amidst Byzantine agents. During the game process, each honest agent is influenced by both randomness and malicious information propagated by Byzantine agents. Additionally, none of the agents have prior knowledge about the number and identities of Byzantine agents. Furthermore, the stochastic local cost function and coupled global constraint function are only revealed to each agent in hindsight at each round. One major challenge in addressing such an issue is the stringent requirement for each honest agent to effectively mitigate the effect of decision variables of Byzantine agents on its local cost functions. To overcome this challenge, a decentralized Byzantine-resilient algorithm for online stochastic generalized Nash equilibrium (SGNE) seeking is developed, which combines variance reduction, dynamic average consensus, and robust aggregation techniques. Moreover, novel resilient versions of system-wide regret and constraint violation are proposed as metrics for evaluating the performance of the online algorithm. Under certain conditions, it is proven that these resilient metrics grow sublinearly over time in expectation. Numerical simulations are conducted to validate the theoretical findings.