# Convergence Analysis of Over-the-Air FL with Compression and Power Control via Clipping

arXiv: https://arxiv.org/abs/2305.11135 · HTML: https://mlsanity.com/paper/2305.11135/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 18 references that are in the map.
- First posted on arXiv 18 May 2023.

## Builds on (most cited first, 13 of 13)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [Federated Learning via Over-the-Air Computation](https://mlsanity.com/paper/1812.11750/) (2018)
- [Federated Learning over Wireless Fading Channels](https://mlsanity.com/paper/1907.09769/) (2019)
- [Qsparse-local-SGD: Distributed SGD with Quantization, Sparsification, and Local Computations](https://mlsanity.com/paper/1906.02367/) (2019)
- [One-Bit Over-the-Air Aggregation for Communication-Efficient Federated Edge Learning: Design and Convergence Analysis](https://mlsanity.com/paper/2001.05713/) (2020)
- [Over-the-Air Federated Learning from Heterogeneous Data](https://mlsanity.com/paper/2009.12787/) (2020)
- [Privacy For Free: Wireless Federated Learning Via Uncoded Transmission With Adaptive Power Control](https://mlsanity.com/paper/2006.05459/) (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)
- [Decentralized Federated Learning via SGD over Wireless D2D Networks](https://mlsanity.com/paper/2002.12507/) (2020)
- [Wireless Federated Langevin Monte Carlo: Repurposing Channel Noise for Bayesian Sampling and Privacy](https://mlsanity.com/paper/2108.07644/) (2021)
- [Communication-Efficient Federated Learning over MIMO Multiple Access Channels](https://mlsanity.com/paper/2206.05723/) (2022)

## Built on by (most cited first, 2 of 2)

- [Pre-Training and Personalized Fine-Tuning via Over-the-Air Federated Meta-Learning: Convergence-Generalization Trade-Offs](https://mlsanity.com/paper/2406.11569/) (2024)
- [Differential Privacy as a Perk: Federated Learning over Multiple-Access Fading Channels with a Multi-Antenna Base Station](https://mlsanity.com/paper/2510.23463/) (2025)

## Abstract (arXiv)

One of the key challenges towards the deployment of over-the-air federated learning (AirFL) is the design of mechanisms that can comply with the power and bandwidth constraints of the shared channel, while causing minimum deterioration to the learning performance as compared to baseline noiseless implementations. For additive white Gaussian noise (AWGN) channels with instantaneous per-device power constraints, prior work has demonstrated the optimality of a power control mechanism based on norm clipping. This was done through the minimization of an upper bound on the optimality gap for smooth learning objectives satisfying the Polyak-Lojasiewicz (PL) condition. In this paper, we make two contributions to the development of AirFL based on norm clipping, which we refer to as AirFL-Clip. First, we provide a convergence bound for AirFLClip that applies to general smooth and non-convex learning objectives. Unlike existing results, the derived bound is free from run-specific parameters, thus supporting an offline evaluation. Second, we extend AirFL-Clip to include Top-k sparsification and linear compression. For this generalized protocol, referred to as AirFL-Clip-Comp, we derive a convergence bound for general smooth and non-convex learning objectives. We argue, and demonstrate via experiments, that the only time-varying quantities present in the bound can be efficiently estimated offline by leveraging the well-studied properties of sparse recovery algorithms.