# Over-the-Air Federated Learning with Retransmissions (Extended Version)

arXiv: https://arxiv.org/abs/2111.10267 · HTML: https://mlsanity.com/paper/2111.10267/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 43 references that are in the map.
- First posted on arXiv 19 Nov 2021.

## Builds on (most cited first, 20 of 20)

- [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)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (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)
- [Broadband Analog Aggregation for Low-Latency Federated Edge Learning (Extended Version)](https://mlsanity.com/paper/1812.11494/) (2018)
- [One-Bit Over-the-Air Aggregation for Communication-Efficient Federated Edge Learning: Design and Convergence Analysis](https://mlsanity.com/paper/2001.05713/) (2020)
- [Towards an Intelligent Edge: Wireless Communication Meets Machine Learning](https://mlsanity.com/paper/1809.00343/) (2018)
- [On Analog Gradient Descent Learning over Multiple Access Fading Channels](https://mlsanity.com/paper/1908.07463/) (2019)
- [Federated Learning via Intelligent Reflecting Surface](https://mlsanity.com/paper/2011.05051/) (2020)
- [Over-the-Air Computation Systems: Optimization, Analysis and Scaling Laws](https://mlsanity.com/paper/1909.00329/) (2019)
- [Private Wireless Federated Learning with Anonymous Over-the-Air Computation](https://mlsanity.com/paper/2011.08579/) (2020)
- [Over-the-air Function Computation in Sensor Networks](https://mlsanity.com/paper/1612.02307/) (2016)
- [Temporal-Structure-Assisted Gradient Aggregation for Over-the-Air Federated Edge Learning](https://mlsanity.com/paper/2103.02270/) (2021)
- [Over-the-Air Computation Systems: Optimal Design with Sum-Power Constraint](https://mlsanity.com/paper/2005.09139/) (2020)
- [Over-the-Air Computation via Intelligent Reflecting Surfaces](https://mlsanity.com/paper/1904.12475/) (2019)
- [Wireless for Machine Learning](https://mlsanity.com/paper/2008.13492/) (2020)
- [Optimized Power Control for Over-the-Air Federated Edge Learning](https://mlsanity.com/paper/2011.05587/) (2020)

## Built on by (most cited first, 1 of 1)

- [A Survey on Over-the-Air Computation](https://mlsanity.com/paper/2210.11350/) (2022)

## Abstract (arXiv)

Motivated by increasing computational capabilities of wireless devices, as well as unprecedented levels of user- and device-generated data, new distributed machine learning (ML) methods have emerged. In the wireless community, Federated Learning (FL) is of particular interest due to its communication efficiency and its ability to deal with the problem of non-IID data. FL training can be accelerated by a wireless communication method called Over-the-Air Computation (AirComp) which harnesses the interference of simultaneous uplink transmissions to efficiently aggregate model updates. However, since AirComp utilizes analog communication, it introduces inevitable estimation errors. In this paper, we study the impact of such estimation errors on the convergence of FL and propose retransmissions as a method to improve FL convergence over resource-constrained wireless networks. First, we derive the optimal AirComp power control scheme with retransmissions over static channels. Then, we investigate the performance of Over-the-Air FL with retransmissions and find two upper bounds on the FL loss function. Finally, we propose a heuristic for selecting the optimal number of retransmissions, which can be calculated before training the ML model. Numerical results demonstrate that the introduction of retransmissions can lead to improved ML performance, without incurring extra costs in terms of communication or computation. Additionally, we provide simulation results on our heuristic which indicate that it can correctly identify the optimal number of retransmissions for different wireless network setups and machine learning problems.