Byzantine-resilient decentralized network learning

Decentralized federated learning based on fully normal nodes has drawn attention in modern statistical learning. However, due to data corruption, device malfunctioning, malicious attacks and some other unexpected behaviors, not all nodes can obey the estimation process and the existing decentralized federated learning methods may fail. An unknown number of abnormal nodes, called Byzantine nodes, arbitrarily deviate from their intended behaviors, send wrong messages to their neighbors and affect all honest nodes across the entire network through passing polluted messages. In this paper, we focus on decentralized federated learning in the presence of Byzantine attacks and then propose a unified Byzantine-resilient framework based on the network gradient descent and several robust aggregation rules. Theoretically, the convergence of the proposed algorithm is guaranteed under some weakly balanced conditions of network structure. The finite-sample performance is studied through simulations under different network topologies and various Byzantine attacks. An application to Communities and Crime Data is also presented.