# Over-the-Air Federated Learning and Optimization

arXiv: https://arxiv.org/abs/2310.10089 · HTML: https://mlsanity.com/paper/2310.10089/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 122 of its 171 references that are in the map.
- First posted on arXiv 16 Oct 2023.

## Builds on (most cited first, 30 of 122)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Federated Learning with Non-IID Data](https://mlsanity.com/paper/1806.00582/) (2018)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [Towards Federated Learning at Scale: System Design](https://mlsanity.com/paper/1902.01046/) (2019)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [Ditto: Fair and Robust Federated Learning Through Personalization](https://mlsanity.com/paper/2012.04221/) (2020)
- [Local SGD Converges Fast and Communicates Little](https://mlsanity.com/paper/1805.09767/) (2018)
- [Towards Personalized Federated Learning](https://mlsanity.com/paper/2103.00710/) (2021)
- [Agnostic Federated Learning](https://mlsanity.com/paper/1902.00146/) (2019)
- [Adaptive Federated Learning in Resource Constrained Edge Computing Systems](https://mlsanity.com/paper/1804.05271/) (2018)
- [Fair Resource Allocation in Federated Learning](https://mlsanity.com/paper/1905.10497/) (2019)
- [A Unified Theory of Decentralized SGD with Changing Topology and Local Updates](https://mlsanity.com/paper/2003.10422/) (2020)
- [FedPAQ: A Communication-Efficient Federated Learning Method with Periodic Averaging and Quantization](https://mlsanity.com/paper/1909.13014/) (2019)
- [Lookahead Optimizer: k steps forward, 1 step back](https://mlsanity.com/paper/1907.08610/) (2019)
- [A Field Guide to Federated Optimization](https://mlsanity.com/paper/2107.06917/) (2021)
- [How to Escape Saddle Points Efficiently](https://mlsanity.com/paper/1703.00887/) (2017)
- [Parallel Restarted SGD with Faster Convergence and Less Communication: Demystifying Why Model Averaging Works for Deep Learning](https://mlsanity.com/paper/1807.06629/) (2018)
- [Tighter Theory for Local SGD on Identical and Heterogeneous Data](https://mlsanity.com/paper/1909.04746/) (2019)
- [A Joint Learning and Communications Framework for Federated Learning over Wireless Networks](https://mlsanity.com/paper/1909.07972/) (2019)
- [Federated Learning via Over-the-Air Computation](https://mlsanity.com/paper/1812.11750/) (2018)
- [Client-Edge-Cloud Hierarchical Federated Learning](https://mlsanity.com/paper/1905.06641/) (2019)
- [Personalized Federated Learning with First Order Model Optimization](https://mlsanity.com/paper/2012.08565/) (2020)
- [Broadband Analog Aggregation for Low-Latency Federated Edge Learning (Extended Version)](https://mlsanity.com/paper/1812.11494/) (2018)
- [Federated Learning over Wireless Fading Channels](https://mlsanity.com/paper/1907.09769/) (2019)

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

- [A Survey on Integrated Sensing, Communication, and Computation](https://mlsanity.com/paper/2408.08074/) (2024)
- [Satellite Federated Edge Learning: Architecture Design and Convergence Analysis](https://mlsanity.com/paper/2404.01875/) (2024)
- [Biased Federated Learning under Wireless Heterogeneity](https://mlsanity.com/paper/2503.06078/) (2025)
- [Optimal Transceiver Design in Over-the-Air Federated Distillation](https://mlsanity.com/paper/2507.15256/) (2025)
- [Federated Learning over Hierarchical Wireless Networks: Training Latency Minimization via Submodel Partitioning](https://mlsanity.com/paper/2310.17890/) (2023)
- [Hierarchical Learning and Computing over Space-Ground Integrated Networks](https://mlsanity.com/paper/2408.14116/) (2024)
- [Non-Convex Over-the-Air Heterogeneous Federated Learning: A Bias-Variance Trade-off](https://mlsanity.com/paper/2510.26722/) (2025)
- [A Green Multi-Attribute Client Selection for Over-The-Air Federated Learning: A Grey-Wolf-Optimizer Approach](https://mlsanity.com/paper/2409.11442/) (2024)
- [SCENE OTA-FD: Self-Centering Noncoherent Estimator for Over-the-Air Federated Distillation](https://mlsanity.com/paper/2602.15326/) (2026)
- [Resource-Element Energy Difference for Noncoherent Over-the-Air Federated Learning](https://mlsanity.com/paper/2605.07263/) (2026)

## Abstract (arXiv)

Federated learning (FL), as an emerging distributed machine learning paradigm, allows a mass of edge devices to collaboratively train a global model while preserving privacy. In this tutorial, we focus on FL via over-the-air computation (AirComp), which is proposed to reduce the communication overhead for FL over wireless networks at the cost of compromising in the learning performance due to model aggregation error arising from channel fading and noise. We first provide a comprehensive study on the convergence of AirComp-based FedAvg (AirFedAvg) algorithms under both strongly convex and non-convex settings with constant and diminishing learning rates in the presence of data heterogeneity. Through convergence and asymptotic analysis, we characterize the impact of aggregation error on the convergence bound and provide insights for system design with convergence guarantees. Then we derive convergence rates for AirFedAvg algorithms for strongly convex and non-convex objectives. For different types of local updates that can be transmitted by edge devices (i.e., local model, gradient, and model difference), we reveal that transmitting local model in AirFedAvg may cause divergence in the training procedure. In addition, we consider more practical signal processing schemes to improve the communication efficiency and further extend the convergence analysis to different forms of model aggregation error caused by these signal processing schemes. Extensive simulation results under different settings of objective functions, transmitted local information, and communication schemes verify the theoretical conclusions.