High-dimensional M-estimation for Byzantine-robust decentralized learning.

In this paper, we focus on robust sparse M -estimation over decentralized networks in the presence of Byzantine attacks. In particular, a decentralized network is modeled as an undirected graph without a central node, while a small fraction of nodes usually behave arbitrarily and send erroneous information due to system breakdowns, cyber attacks and so on. To address the Byzantine issue, some pre-determined robust aggregation rules are applied. Moreover, the gradient tracking and proximal algorithm are combined to ensure convergence and sparsity simultaneously. Theoretically, our proposed algorithms are provably robust against Byzantine attacks and achieve linear convergence rates. The finite-sample performance is studied through numerical experiments under various settings and an application to Communities and Crime Data is also presented. [ABSTRACT FROM AUTHOR]