# Adaptive Federated Learning Over the Air

arXiv: https://arxiv.org/abs/2403.06528 · HTML: https://mlsanity.com/paper/2403.06528/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 59 references that are in the map.
- First posted on arXiv 11 Mar 2024.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [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)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [Ensemble Distillation for Robust Model Fusion in Federated Learning](https://mlsanity.com/paper/2006.07242/) (2020)
- [Federated Learning via Over-the-Air Computation](https://mlsanity.com/paper/1812.11750/) (2018)
- [Broadband Analog Aggregation for Low-Latency Federated Edge Learning (Extended Version)](https://mlsanity.com/paper/1812.11494/) (2018)
- [AdaGrad stepsizes: Sharp convergence over nonconvex landscapes](https://mlsanity.com/paper/1806.01811/) (2018)
- [A Simple Convergence Proof of Adam and Adagrad](https://mlsanity.com/paper/2003.02395/) (2020)
- [Scheduling Policies for Federated Learning in Wireless Networks](https://mlsanity.com/paper/1908.06287/) (2019)
- [Federated Learning for Wireless Communications: Motivation, Opportunities and Challenges](https://mlsanity.com/paper/1908.06847/) (2019)
- [On Analog Gradient Descent Learning over Multiple Access Fading Channels](https://mlsanity.com/paper/1908.07463/) (2019)
- [Optimized Power Control Design for Over-the-Air Federated Edge Learning](https://mlsanity.com/paper/2106.09316/) (2021)
- [Mobility-Aware Cluster Federated Learning in Hierarchical Wireless Networks](https://mlsanity.com/paper/2108.09103/) (2021)
- [Federated Edge Learning with Misaligned Over-The-Air Computation](https://mlsanity.com/paper/2102.13604/) (2021)
- [A Survey on Over-the-Air Computation](https://mlsanity.com/paper/2210.11350/) (2022)
- [Fast Convergence Algorithm for Analog Federated Learning](https://mlsanity.com/paper/2011.06658/) (2020)
- [Fed-GraB: Federated Long-tailed Learning with Self-Adjusting Gradient Balancer](https://mlsanity.com/paper/2310.07587/) (2023)
- [Turning Channel Noise into an Accelerator for Over-the-Air Principal Component Analysis](https://mlsanity.com/paper/2104.10095/) (2021)
- [Accelerated Gradient Descent Learning over Multiple Access Fading Channels](https://mlsanity.com/paper/2107.12452/) (2021)
- [FedCompass: Efficient Cross-Silo Federated Learning on Heterogeneous Client Devices using a Computing Power Aware Scheduler](https://mlsanity.com/paper/2309.14675/) (2023)
- [Over-the-Air Federated Learning via Second-Order Optimization](https://mlsanity.com/paper/2203.15488/) (2022)
- [Over-the-Air Aggregation for Federated Learning: Waveform Superposition and Prototype Validation](https://mlsanity.com/paper/2110.14285/) (2021)
- [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 with Joint Adaptive Computation and Power Control](https://mlsanity.com/paper/2205.05867/) (2022)
- [Edge Intelligence Over the Air: Two Faces of Interference in Federated Learning](https://mlsanity.com/paper/2306.10299/) (2023)
- [Optimal Receive Filter Design for Misaligned Over-the-Air Computation](https://mlsanity.com/paper/2309.16033/) (2023)
- [Personalizing Federated Learning with Over-the-Air Computations](https://mlsanity.com/paper/2302.12509/) (2023)

## Built on by (most cited first, 4 of 4)

- [Energy-Efficient Over-the-Air Federated Learning via Pinching Antenna Systems](https://mlsanity.com/paper/2602.14250/) (2026)
- [Resource-Element Energy Difference for Noncoherent Over-the-Air Federated Learning](https://mlsanity.com/paper/2605.07263/) (2026)
- [Federated learning with heavy-tailed gradient noise and communication noise: a variance-reduction based algorithm](https://mlsanity.com/paper/2606.22466/) (2026)
- [Channel-Adaptive Robust Aggregation for Over-the-Air Federated Learning in Heterogeneous Networks](https://mlsanity.com/paper/2607.04218/) (2026)

## Abstract (arXiv)

We propose a federated version of adaptive gradient methods, particularly AdaGrad and Adam, within the framework of over-the-air model training. This approach capitalizes on the inherent superposition property of wireless channels, facilitating fast and scalable parameter aggregation. Meanwhile, it enhances the robustness of the model training process by dynamically adjusting the stepsize in accordance with the global gradient update. We derive the convergence rate of the training algorithms, encompassing the effects of channel fading and interference, for a broad spectrum of nonconvex loss functions. Our analysis shows that the AdaGrad-based algorithm converges to a stationary point at the rate of O( ln(T) / T^ 1 - frac1α   ), where α represents the tail index of the electromagnetic interference. This result indicates that the level of heavy-tailedness in interference distribution plays a crucial role in the training efficiency: the heavier the tail, the slower the algorithm converges. In contrast, an Adam-like algorithm converges at the O( 1/T ) rate, demonstrating its advantage in expediting the model training process. We conduct extensive experiments that corroborate our theoretical findings and affirm the practical efficacy of our proposed federated adaptive gradient methods.