# BEV-SGD: Best Effort Voting SGD for Analog Aggregation Based Federated Learning against Byzantine Attackers

arXiv: https://arxiv.org/abs/2110.09660 · HTML: https://mlsanity.com/paper/2110.09660/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 57 references that are in the map.
- First posted on arXiv 18 Oct 2021.

## Builds on (most cited first, 30 of 31)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [Byzantine-Robust Distributed Learning: Towards Optimal Statistical Rates](https://mlsanity.com/paper/1803.01498/) (2018)
- [signSGD: Compressed Optimisation for Non-Convex Problems](https://mlsanity.com/paper/1802.04434/) (2018)
- [Deep Gradient Compression: Reducing the Communication Bandwidth for Distributed Training](https://mlsanity.com/paper/1712.01887/) (2017)
- [The Hidden Vulnerability of Distributed Learning in Byzantium](https://mlsanity.com/paper/1802.07927/) (2018)
- [A Joint Learning and Communications Framework for Federated Learning over Wireless Networks](https://mlsanity.com/paper/1909.07972/) (2019)
- [Sparse Communication for Distributed Gradient Descent](https://mlsanity.com/paper/1704.05021/) (2017)
- [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)
- [QSGD: Communication-Efficient SGD via Gradient Quantization and Encoding](https://mlsanity.com/paper/1610.02132/) (2016)
- [One-Bit Over-the-Air Aggregation for Communication-Efficient Federated Edge Learning: Design and Convergence Analysis](https://mlsanity.com/paper/2001.05713/) (2020)
- [Cooperative SGD: A unified Framework for the Design and Analysis of Communication-Efficient SGD Algorithms](https://mlsanity.com/paper/1808.07576/) (2018)
- [LAG: Lazily Aggregated Gradient for Communication-Efficient Distributed Learning](https://mlsanity.com/paper/1805.09965/) (2018)
- [Towards an Intelligent Edge: Wireless Communication Meets Machine Learning](https://mlsanity.com/paper/1809.00343/) (2018)
- [Federated Variance-Reduced Stochastic Gradient Descent with Robustness to Byzantine Attacks](https://mlsanity.com/paper/1912.12716/) (2019)
- [Privacy For Free: Wireless Federated Learning Via Uncoded Transmission With Adaptive Power Control](https://mlsanity.com/paper/2006.05459/) (2020)
- [Zeno++: Robust Fully Asynchronous SGD](https://mlsanity.com/paper/1903.07020/) (2019)
- [Learning Rate Optimization for Federated Learning Exploiting Over-the-air Computation](https://mlsanity.com/paper/2102.02946/) (2021)
- [Energy-Aware Analog Aggregation for Federated Learning with Redundant Data](https://mlsanity.com/paper/1911.00188/) (2019)
- [Fast Convergence Algorithm for Analog Federated Learning](https://mlsanity.com/paper/2011.06658/) (2020)
- [Edge Federated Learning Via Unit-Modulus Over-The-Air Computation](https://mlsanity.com/paper/2101.12051/) (2021)
- [Joint Optimization of Communications and Federated Learning Over the Air](https://mlsanity.com/paper/2104.03490/) (2021)
- [1-Bit Compressive Sensing for Efficient Federated Learning Over the Air](https://mlsanity.com/paper/2103.16055/) (2021)
- [Collaborative Machine Learning at the Wireless Edge with Blind Transmitters](https://mlsanity.com/paper/1907.03909/) (2019)
- [Zeno: Distributed Stochastic Gradient Descent with Suspicion-based Fault-tolerance](https://mlsanity.com/paper/1805.10032/) (2018)
- [Secure Distributed On-Device Learning Networks With Byzantine Adversaries](https://mlsanity.com/paper/1906.00887/) (2019)
- [Optimized Power Control for Over-the-Air Computation in Fading Channels](https://mlsanity.com/paper/1906.06858/) (2019)

## Built on by (most cited first, 6 of 6)

- [A Survey on Over-the-Air Computation](https://mlsanity.com/paper/2210.11350/) (2022)
- [Over-The-Air Federated Learning: Status Quo, Open Challenges, and Future Directions](https://mlsanity.com/paper/2307.00974/) (2023)
- [Spectrum Breathing: Protecting Over-the-Air Federated Learning Against Interference](https://mlsanity.com/paper/2305.05933/) (2023)
- [Federated Learning Resilient to Byzantine Attacks and Data Heterogeneity](https://mlsanity.com/paper/2403.13374/) (2024)
- [Distributed Swarm Learning for Edge Internet of Things](https://mlsanity.com/paper/2403.20188/) (2024)
- [Byzantine-Resilient Over-the-Air Federated Learning under Zero-Trust Architecture](https://mlsanity.com/paper/2503.18284/) (2025)

## Abstract (arXiv)

As a promising distributed learning technology, analog aggregation based federated learning over the air (FLOA) provides high communication efficiency and privacy provisioning under the edge computing paradigm. When all edge devices (workers) simultaneously upload their local updates to the parameter server (PS) through commonly shared time-frequency resources, the PS obtains the averaged update only rather than the individual local ones. While such a concurrent transmission and aggregation scheme reduces the latency and communication costs, it unfortunately renders FLOA vulnerable to Byzantine attacks. Aiming at Byzantine-resilient FLOA, this paper starts from analyzing the channel inversion (CI) mechanism that is widely used for power control in FLOA. Our theoretical analysis indicates that although CI can achieve good learning performance in the benign scenarios, it fails to work well with limited defensive capability against Byzantine attacks. Then, we propose a novel scheme called the best effort voting (BEV) power control policy that is integrated with stochastic gradient descent (SGD). Our BEV-SGD enhances the robustness of FLOA to Byzantine attacks, by allowing all the workers to send their local updates at their maximum transmit power. Under worst-case attacks, we derive the expected convergence rates of FLOA with CI and BEV power control policies, respectively. The rate comparison reveals that our BEV-SGD outperforms its counterpart with CI in terms of better convergence behavior, which is verified by experimental simulations.