DONE: Distributed Approximate Newton-type Method for Federated Edge Learning

TL;DR

DONE is a distributed approximate Newton method designed for federated edge learning, achieving fast convergence and communication efficiency in heterogeneous, non-i.i.d. data environments.

Contribution

The paper introduces DONE, a novel distributed Newton-type algorithm that converges linearly-quadratically and reduces communication costs in federated edge learning.

Findings

DONE attains performance comparable to Newton's method.

Fewer communication iterations than distributed gradient descent.

Outperforms DANE and FEDL in non-quadratic loss scenarios.

Abstract

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.