A Dynamically Weighted ADMM Framework for Byzantine Resilience

TL;DR

This paper introduces DW-ADMM, a new adaptive algorithm that enhances the robustness of distributed optimization against Byzantine faults by dynamically adjusting weights during communication.

Contribution

The paper proposes DW-ADMM, a novel variant of ADMM that uses dynamic weights to improve resilience against Byzantine attacks in distributed consensus optimization.

Findings

DW-ADMM achieves solutions close to traditional ADMM in fault-free scenarios.

The method guarantees bounded solutions despite Byzantine threats.

Numerical simulations demonstrate the effectiveness of DW-ADMM.

Abstract

The alternating direction of multipliers method (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 work 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. 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 an illustrative numerical simulation.