# Over-the-Air Federated Learning from Heterogeneous Data

arXiv: https://arxiv.org/abs/2009.12787 · HTML: https://mlsanity.com/paper/2009.12787/

## Key facts

- Cited by 73 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Sep 2020.

## Built on by (most cited first, 30 of 73)

- [Communication-Efficient Stochastic Zeroth-Order Optimization for Federated Learning](https://mlsanity.com/paper/2201.09531/) (2022)
- [Semi-Decentralized Federated Learning with Cooperative D2D Local Model Aggregations](https://mlsanity.com/paper/2103.10481/) (2021)
- [Federated Learning: A Signal Processing Perspective](https://mlsanity.com/paper/2103.17150/) (2021)
- [Dynamic Scheduling for Over-the-Air Federated Edge Learning with Energy Constraints](https://mlsanity.com/paper/2106.00490/) (2021)
- [Joint Privacy Enhancement and Quantization in Federated Learning](https://mlsanity.com/paper/2208.10888/) (2022)
- [Federated Edge Learning with Misaligned Over-The-Air Computation](https://mlsanity.com/paper/2102.13604/) (2021)
- [Fusion of Federated Learning and Industrial Internet of Things: A Survey](https://mlsanity.com/paper/2101.00798/) (2021)
- [Over-The-Air Federated Learning: Status Quo, Open Challenges, and Future Directions](https://mlsanity.com/paper/2307.00974/) (2023)
- [Edge Federated Learning Via Unit-Modulus Over-The-Air Computation](https://mlsanity.com/paper/2101.12051/) (2021)
- [On the Convergence of Decentralized Federated Learning Under Imperfect Information Sharing](https://mlsanity.com/paper/2303.10695/) (2023)
- [Accelerated Gradient Descent Learning over Multiple Access Fading Channels](https://mlsanity.com/paper/2107.12452/) (2021)
- [Non-IID data in Federated Learning: A Survey with Taxonomy, Metrics, Methods, Frameworks and Future Directions](https://mlsanity.com/paper/2411.12377/) (2024)
- [Hierarchical Over-the-Air Federated Edge Learning](https://mlsanity.com/paper/2112.11167/) (2021)
- [Over-the-Air Federated Edge Learning with Hierarchical Clustering](https://mlsanity.com/paper/2207.09232/) (2022)
- [Over-the-Air Computation Based on Balanced Number Systems for Federated Edge Learning](https://mlsanity.com/paper/2210.07012/) (2022)
- [Over-the-Air Federated Learning and Optimization](https://mlsanity.com/paper/2310.10089/) (2023)
- [Over-the-Air Federated Learning with Joint Adaptive Computation and Power Control](https://mlsanity.com/paper/2205.05867/) (2022)
- [Spectrum Breathing: Protecting Over-the-Air Federated Learning Against Interference](https://mlsanity.com/paper/2305.05933/) (2023)
- [Channel and Gradient-Importance Aware Device Scheduling for Over-the-Air Federated Learning](https://mlsanity.com/paper/2305.16854/) (2023)
- [Federated Learning over Noisy Channels: Convergence Analysis and Design Examples](https://mlsanity.com/paper/2101.02198/) (2021)
- [Over-the-Air Federated Multi-Task Learning Over MIMO Multiple Access Channels](https://mlsanity.com/paper/2112.13603/) (2021)
- [Client Selection for Generalization in Accelerated Federated Learning: A Multi-Armed Bandit Approach](https://mlsanity.com/paper/2303.10373/) (2023)
- [AirMixML: Over-the-Air Data Mixup for Inherently Privacy-Preserving Edge Machine Learning](https://mlsanity.com/paper/2105.00395/) (2021)
- [Robust Federated Learning via Over-The-Air Computation](https://mlsanity.com/paper/2111.01221/) (2021)
- [Federated Multi-Armed Bandits Under Byzantine Attacks](https://mlsanity.com/paper/2205.04134/) (2022)
- [Robust Federated Learning with Connectivity Failures: A Semi-Decentralized Framework with Collaborative Relaying](https://mlsanity.com/paper/2202.11850/) (2022)
- [Over-the-Air Federated Learning with Privacy Protection via Correlated Additive Perturbations](https://mlsanity.com/paper/2210.02235/) (2022)
- [Over-The-Air Federated Learning under Byzantine Attacks](https://mlsanity.com/paper/2205.02949/) (2022)
- [Over-the-Air Computation over Balanced Numerals](https://mlsanity.com/paper/2209.11004/) (2022)
- [Improved Convergence Analysis and SNR Control Strategies for Federated Learning in the Presence of Noise](https://mlsanity.com/paper/2307.07406/) (2023)

## Abstract (arXiv)

Federated learning (FL) is a framework for distributed learning of centralized models. In FL, a set of edge devices train a model using their local data, while repeatedly exchanging their trained updates with a central server. This procedure allows tuning a centralized model in a distributed fashion without having the users share their possibly private data. In this paper, we focus on over-the-air (OTA) FL, which has been suggested recently to reduce the communication overhead of FL due to the repeated transmissions of the model updates by a large number of users over the wireless channel. In OTA FL, all users simultaneously transmit their updates as analog signals over a multiple access channel, and the server receives a superposition of the analog transmitted signals. However, this approach results in the channel noise directly affecting the optimization procedure, which may degrade the accuracy of the trained model. We develop a Convergent OTA FL (COTAF) algorithm which enhances the common local stochastic gradient descent (SGD) FL algorithm, introducing precoding at the users and scaling at the server, which gradually mitigates the effect of the noise. We analyze the convergence of COTAF to the loss minimizing model and quantify the effect of a statistically heterogeneous setup, i.e. when the training data of each user obeys a different distribution. Our analysis reveals the ability of COTAF to achieve a convergence rate similar to that achievable over error-free channels. Our simulations demonstrate the improved convergence of COTAF over vanilla OTA local SGD for training using non-synthetic datasets. Furthermore, we numerically show that the precoding induced by COTAF notably improves the convergence rate and the accuracy of models trained via OTA FL.