# Biased Over-the-Air Federated Learning under Wireless Heterogeneity

arXiv: https://arxiv.org/abs/2403.19849 · HTML: https://mlsanity.com/paper/2403.19849/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 21 references that are in the map.
- First posted on arXiv 28 Mar 2024.

## Builds on (most cited first, 18 of 18)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [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)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Federated Learning in Mobile Edge Networks: A Comprehensive Survey](https://mlsanity.com/paper/1909.11875/) (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)
- [Federated Learning over Wireless Fading Channels](https://mlsanity.com/paper/1907.09769/) (2019)
- [Scheduling Policies for Federated Learning in Wireless Networks](https://mlsanity.com/paper/1908.06287/) (2019)
- [Distributed Learning in Wireless Networks: Recent Progress and Future Challenges](https://mlsanity.com/paper/2104.02151/) (2021)
- [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)
- [Blind Federated Edge Learning](https://mlsanity.com/paper/2010.10030/) (2020)
- [Multi-Stage Hybrid Federated Learning over Large-Scale D2D-Enabled Fog Networks](https://mlsanity.com/paper/2007.09511/) (2020)
- [Distributed Machine Learning for Wireless Communication Networks: Techniques, Architectures, and Applications](https://mlsanity.com/paper/2012.01489/) (2020)
- [Analog-digital Scheduling for Federated Learning: A Communication-Efficient Approach](https://mlsanity.com/paper/2402.00318/) (2024)
- [Decentralized Federated Learning via Non-Coherent Over-the-Air Consensus](https://mlsanity.com/paper/2210.15806/) (2022)

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

- [Biased Federated Learning under Wireless Heterogeneity](https://mlsanity.com/paper/2503.06078/) (2025)
- [Non-Convex Over-the-Air Heterogeneous Federated Learning: A Bias-Variance Trade-off](https://mlsanity.com/paper/2510.26722/) (2025)

## Abstract (arXiv)

Recently, Over-the-Air (OTA) computation has emerged as a promising federated learning (FL) paradigm that leverages the waveform superposition properties of the wireless channel to realize fast model updates. Prior work focused on the OTA device ``pre-scaler" design under homogeneous wireless conditions, in which devices experience the same average path loss, resulting in zero-bias solutions. Yet, zero-bias designs are limited by the device with the worst average path loss and hence may perform poorly in heterogeneous wireless settings. In this scenario, there may be a benefit in designing biased solutions, in exchange for a lower variance in the model updates. To optimize this trade-off, we study the design of OTA device pre-scalers by focusing on the OTA-FL convergence. We derive an upper bound on the model ``optimality error", which explicitly captures the effect of bias and variance in terms of the choice of the pre-scalers. Based on this bound, we identify two solutions of interest: minimum noise variance, and minimum noise variance zero-bias solutions. Numerical evaluations show that using OTA device pre-scalers that minimize the variance of FL updates, while allowing a small bias, can provide high gains over existing schemes.