A Dynamically Weighted ADMM Framework for Byzantine Resilience

The alternating direction method of multipliers (ADMM) is a popular method to solve distributed consensus optimization utilizing efficient communication among various nodes in the network. However, in the presence of faulty or attacked nodes, even a small perturbation (or sharing false data) during the communication can lead to divergence of the solution. To address this issue, in this letter we consider ADMM under the effect of Byzantine threat, where an unknown subset of nodes is subject to Byzantine attacks or faults. We propose Dynamically Weighted ADMM (DW-ADMM), a novel variant of ADMM that uses dynamic weights on the edges of the network, thus promoting resilient distributed optimization in settings without central coordination. We establish that the proposed method (i) produces a nearly identical solution to conventional ADMM in the error-free case, and (ii) guarantees a bounded solution with respect to the global minimizer, even under Byzantine threat. Finally, we demonstrate the effectiveness of our proposed algorithm using illustrative numerical simulations.