# Machine Learning at the Wireless Edge: Distributed Stochastic Gradient Descent Over-the-Air

arXiv: https://arxiv.org/abs/1901.00844 · HTML: https://mlsanity.com/paper/1901.00844/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jan 2019.

## Built on by (most cited first, 10 of 10)

- [A Comprehensive Survey of Deep Transfer Learning for Anomaly Detection in Industrial Time Series: Methods, Applications, and Directions](https://mlsanity.com/paper/2307.05638/) (2023)
- [Communication-Efficient Federated Learning via Quantized Compressed Sensing](https://mlsanity.com/paper/2111.15071/) (2021)
- [A Survey on Approximate Edge AI for Energy Efficient Autonomous Driving Services](https://mlsanity.com/paper/2304.14271/) (2023)
- [Over-the-Air Ensemble Inference with Model Privacy](https://mlsanity.com/paper/2202.03129/) (2022)
- [Federated Learning over Noisy Channels: Convergence Analysis and Design Examples](https://mlsanity.com/paper/2101.02198/) (2021)
- [Communication and Energy Efficient Wireless Federated Learning with Intrinsic Privacy](https://mlsanity.com/paper/2304.07460/) (2023)
- [Fundamental limits of over-the-air optimization: Are analog schemes optimal?](https://mlsanity.com/paper/2109.05222/) (2021)
- [Federated learning and next generation wireless communications: A survey on bidirectional relationship](https://mlsanity.com/paper/2110.07649/) (2021)
- [Federated Learning in Wireless Networks via Over-the-Air Computations](https://mlsanity.com/paper/2305.04630/) (2023)
- [Federated Channel Learning for Intelligent Reflecting Surfaces With Fewer Pilot Signals](https://mlsanity.com/paper/2205.03196/) (2022)

## Abstract (arXiv)

We study federated machine learning (ML) at the wireless edge, where power- and bandwidth-limited wireless devices with local datasets carry out distributed stochastic gradient descent (DSGD) with the help of a remote parameter server (PS). Standard approaches assume separate computation and communication, where local gradient estimates are compressed and transmitted to the PS over orthogonal links. Following this digital approach, we introduce D-DSGD, in which the wireless devices employ gradient quantization and error accumulation, and transmit their gradient estimates to the PS over a multiple access channel (MAC). We then introduce a novel analog scheme, called A-DSGD, which exploits the additive nature of the wireless MAC for over-the-air gradient computation, and provide convergence analysis for this approach. In A-DSGD, the devices first sparsify their gradient estimates, and then project them to a lower dimensional space imposed by the available channel bandwidth. These projections are sent directly over the MAC without employing any digital code. Numerical results show that A-DSGD converges faster than D-DSGD thanks to its more efficient use of the limited bandwidth and the natural alignment of the gradient estimates over the channel. The improvement is particularly compelling at low power and low bandwidth regimes. We also illustrate for a classification problem that, A-DSGD is more robust to bias in data distribution across devices, while D-DSGD significantly outperforms other digital schemes in the literature. We also observe that both D-DSGD and A-DSGD perform better by increasing the number of devices (while keeping the total dataset size constant), showing their ability in harnessing the computation power of edge devices.