D3: Dual-Domain Defenses for Byzantine-Resilient Decentralized Resource Allocation

This paper considers the problem of decentralized resource allocation in the presence of Byzantine attacks. Such attacks occur when an unknown number of malicious agents send random or carefully crafted messages to their neighbors, aiming to prevent the honest agents from reaching the optimal resource allocation strategy. We characterize these malicious behaviors with the classical Byzantine attacks model, and propose a class of Byzantine-resilient decentralized resource allocation algorithms augmented with dual-domain defenses. The honest agents receive messages containing the (possibly malicious) dual variables from their neighbors at each iteration, and filter these messages with robust aggregation rules. Theoretically, we prove that the proposed algorithms converge to a neighborhood of the optimal resource allocation strategy, given that the robust aggregation rules are properly designed. Numerical experiments are conducted to corroborate the theoretical results.