Robust Federated Learning Using ADMM in the Presence of Data Falsifying Byzantines

In this paper, we consider the problem of federated (or decentralized) learning using ADMM with multiple agents. We consider a scenario where a certain fraction of agents (referred to as Byzantines) provide falsified data to the system. In this context, we study the convergence behavior of the decentralized ADMM algorithm. We show that ADMM converges linearly to a neighborhood of the solution to the problem under certain conditions. We next provide guidelines for network structure design to achieve faster convergence. Next, we provide necessary conditions on the falsified updates for exact convergence to the true solution. To tackle the data falsification problem, we propose a robust variant of ADMM. We also provide simulation results to validate the analysis and show the resilience of the proposed algorithm to Byzantines.