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

arXiv: https://arxiv.org/abs/2012.05625 · HTML: https://mlsanity.com/paper/2012.05625/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Dec 2020.

## Built on by (most cited first, 8 of 8)

- [SHED: A Newton-type algorithm for federated learning based on incremental Hessian eigenvector sharing](https://mlsanity.com/paper/2202.05800/) (2022)
- [Fed-Sophia: A Communication-Efficient Second-Order Federated Learning Algorithm](https://mlsanity.com/paper/2406.06655/) (2024)
- [Review of Mathematical Optimization in Federated Learning](https://mlsanity.com/paper/2412.01630/) (2024)
- [FAGH: Accelerating Federated Learning with Approximated Global Hessian](https://mlsanity.com/paper/2403.11041/) (2024)
- [Network-GIANT: Fully distributed Newton-type optimization via harmonic Hessian consensus](https://mlsanity.com/paper/2305.07898/) (2023)
- [Q-SHED: Distributed Optimization at the Edge via Hessian Eigenvectors Quantization](https://mlsanity.com/paper/2305.10852/) (2023)
- [Scalable and Resource-Efficient Second-Order Federated Learning via Over-the-Air Aggregation](https://mlsanity.com/paper/2410.07662/) (2024)
- [Accelerated Training of Federated Learning via Second-Order Methods](https://mlsanity.com/paper/2505.23588/) (2025)

## Abstract (arXiv)

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.