  There is growing interest in applying distributed machine learning to edge
computing, forming federated edge learning. Federated edge learning faces
non-i.i.d. and heterogeneous data, and the communication between edge workers,
possibly through distant locations and with unstable wireless networks, is more
costly than their local computational overhead. In this work, we propose DONE,
a distributed approximate Newton-type algorithm with fast convergence rate for
communication-efficient federated edge learning. First, with strongly convex
and smooth loss functions, DONE approximates the Newton direction in a
distributed manner using the classical Richardson iteration on each edge
worker. Second, we prove that DONE has linear-quadratic convergence and analyze
its communication complexities. Finally, the experimental results with
non-i.i.d. and heterogeneous data show that DONE attains a comparable
performance to the Newton's method. Notably, DONE requires fewer communication
iterations compared to distributed gradient descent and outperforms DANE and
FEDL, state-of-the-art approaches, in the case of non-quadratic loss functions.
