# Over-the-Air Computation Aided Federated Learning with the Aggregation of Normalized Gradient

arXiv: https://arxiv.org/abs/2308.09082 · HTML: https://mlsanity.com/paper/2308.09082/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 26 references that are in the map.
- First posted on arXiv 17 Aug 2023.

## Builds on (most cited first, 21 of 21)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Federated Learning via Over-the-Air Computation](https://mlsanity.com/paper/1812.11750/) (2018)
- [The Roadmap to 6G -- AI Empowered Wireless Networks](https://mlsanity.com/paper/1904.11686/) (2019)
- [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)
- [Fast-Convergent Federated Learning](https://mlsanity.com/paper/2007.13137/) (2020)
- [Federated Learning over Wireless Device-to-Device Networks: Algorithms and Convergence Analysis](https://mlsanity.com/paper/2101.12704/) (2021)
- [Optimized Power Control Design for Over-the-Air Federated Edge Learning](https://mlsanity.com/paper/2106.09316/) (2021)
- [Blind Federated Edge Learning](https://mlsanity.com/paper/2010.10030/) (2020)
- [Dynamic Scheduling for Over-the-Air Federated Edge Learning with Energy Constraints](https://mlsanity.com/paper/2106.00490/) (2021)
- [Reconfigurable Intelligent Surface Enabled Federated Learning: A Unified Communication-Learning Design Approach](https://mlsanity.com/paper/2011.10282/) (2020)
- [Over-the-Air Computation Systems: Optimization, Analysis and Scaling Laws](https://mlsanity.com/paper/1909.00329/) (2019)
- [Convergence Analysis and System Design for Federated Learning over Wireless Networks](https://mlsanity.com/paper/2105.00872/) (2021)
- [Edge Federated Learning Via Unit-Modulus Over-The-Air Computation](https://mlsanity.com/paper/2101.12051/) (2021)
- [Adaptive Transmission Scheduling in Wireless Networks for Asynchronous Federated Learning](https://mlsanity.com/paper/2103.01422/) (2021)
- [Hybrid Beamforming for Massive MIMO Over-the-Air Computation](https://mlsanity.com/paper/2006.04560/) (2020)
- [Temporal-Structure-Assisted Gradient Aggregation for Over-the-Air Federated Edge Learning](https://mlsanity.com/paper/2103.02270/) (2021)
- [Over-the-Air Statistical Estimation](https://mlsanity.com/paper/2103.04014/) (2021)
- [Energy-efficient Resource Allocation for Mobile Edge Computing Aided by Multiple Relays](https://mlsanity.com/paper/2004.03821/) (2020)

## Abstract (arXiv)

Over-the-air computation is a communication-efficient solution for federated learning (FL). In such a system, iterative procedure is performed: Local gradient of private loss function is updated, amplified and then transmitted by every mobile device; the server receives the aggregated gradient all-at-once, generates and then broadcasts updated model parameters to every mobile device. In terms of amplification factor selection, most related works suppose the local gradient's maximal norm always happens although it actually fluctuates over iterations, which may degrade convergence performance. To circumvent this problem, we propose to turn local gradient to be normalized one before amplifying it. Under our proposed method, when the loss function is smooth, we prove our proposed method can converge to stationary point at sub-linear rate. In case of smooth and strongly convex loss function, we prove our proposed method can achieve minimal training loss at linear rate with any small positive tolerance. Moreover, a tradeoff between convergence rate and the tolerance is discovered. To speedup convergence, problems optimizing system parameters are also formulated for above two cases. Although being non-convex, optimal solution with polynomial complexity of the formulated problems are derived. Experimental results show our proposed method can outperform benchmark methods on convergence performance.