# Accelerated Gradient Descent Learning over Multiple Access Fading Channels

arXiv: https://arxiv.org/abs/2107.12452 · HTML: https://mlsanity.com/paper/2107.12452/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 58 references that are in the map.
- First posted on arXiv 26 Jul 2021.

## Builds on (most cited first, 19 of 19)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Optimization: Distributed Machine Learning for On-Device Intelligence](https://mlsanity.com/paper/1610.02527/) (2016)
- [A Joint Learning and Communications Framework for Federated Learning over Wireless Networks](https://mlsanity.com/paper/1909.07972/) (2019)
- [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)
- [Hierarchical Federated Learning Across Heterogeneous Cellular Networks](https://mlsanity.com/paper/1909.02362/) (2019)
- [LAG: Lazily Aggregated Gradient for Communication-Efficient Distributed Learning](https://mlsanity.com/paper/1805.09965/) (2018)
- [Over-the-Air Federated Learning from Heterogeneous Data](https://mlsanity.com/paper/2009.12787/) (2020)
- [On Analog Gradient Descent Learning over Multiple Access Fading Channels](https://mlsanity.com/paper/1908.07463/) (2019)
- [Wireless Federated Learning with Local Differential Privacy](https://mlsanity.com/paper/2002.05151/) (2020)
- [Federated Learning: A Signal Processing Perspective](https://mlsanity.com/paper/2103.17150/) (2021)
- [Wireless Federated Distillation for Distributed Edge Learning with Heterogeneous Data](https://mlsanity.com/paper/1907.02745/) (2019)
- [Energy-Efficient Radio Resource Allocation for Federated Edge Learning](https://mlsanity.com/paper/1907.06040/) (2019)
- [Scheduled Restart Momentum for Accelerated Stochastic Gradient Descent](https://mlsanity.com/paper/2002.10583/) (2020)
- [Energy-Aware Analog Aggregation for Federated Learning with Redundant Data](https://mlsanity.com/paper/1911.00188/) (2019)
- [Communication Efficient Federated Learning over Multiple Access Channels](https://mlsanity.com/paper/2001.08737/) (2020)
- [Collaborative Machine Learning at the Wireless Edge with Blind Transmitters](https://mlsanity.com/paper/1907.03909/) (2019)
- [Optimizing Over-the-Air Computation in IRS-Aided C-RAN Systems](https://mlsanity.com/paper/2004.09168/) (2020)
- [Distributed Sparse SGD with Majority Voting](https://mlsanity.com/paper/2011.06495/) (2020)

## Built on by (most cited first, 14 of 14)

- [Communication-Efficient Stochastic Zeroth-Order Optimization for Federated Learning](https://mlsanity.com/paper/2201.09531/) (2022)
- [A Survey on Over-the-Air Computation](https://mlsanity.com/paper/2210.11350/) (2022)
- [Over-the-Air Federated Learning and Optimization](https://mlsanity.com/paper/2310.10089/) (2023)
- [Client Selection for Generalization in Accelerated Federated Learning: A Multi-Armed Bandit Approach](https://mlsanity.com/paper/2303.10373/) (2023)
- [Federated Learning via Lattice Joint Source-Channel Coding](https://mlsanity.com/paper/2403.01023/) (2024)
- [Compute-Update Federated Learning: A Lattice Coding Approach Over-the-Air](https://mlsanity.com/paper/2409.06343/) (2024)
- [Over-the-Air Federated Learning via Weighted Aggregation](https://mlsanity.com/paper/2409.07822/) (2024)
- [AirFL-Mem: Improving Communication-Learning Trade-Off by Long-Term Memory](https://mlsanity.com/paper/2310.16606/) (2023)
- [Adaptive Federated Learning Over the Air](https://mlsanity.com/paper/2403.06528/) (2024)
- [Over-the-Air Federated Learning: Rethinking Edge AI Through Signal Processing](https://mlsanity.com/paper/2512.03719/) (2025)
- [Sparse Training for Federated Learning with Regularized Error Correction](https://mlsanity.com/paper/2312.13795/) (2023)
- [Accelerating Wireless Federated Learning via Nesterov's Momentum and Distributed Principle Component Analysis](https://mlsanity.com/paper/2303.17885/) (2023)
- [PolarAir: A Compressed Sensing Scheme for Over-the-Air Federated Learning](https://mlsanity.com/paper/2301.10110/) (2023)
- [A Masked Pruning Approach for Dimensionality Reduction in Communication-Efficient Federated Learning Systems](https://mlsanity.com/paper/2312.03889/) (2023)

## Abstract (arXiv)

We consider a distributed learning problem in a wireless network, consisting of N distributed edge devices and a parameter server (PS). The objective function is a sum of the edge devices' local loss functions, who aim to train a shared model by communicating with the PS over multiple access channels (MAC). This problem has attracted a growing interest in distributed sensing systems, and more recently in federated learning, known as over-the-air computation. In this paper, we develop a novel Accelerated Gradient-descent Multiple Access (AGMA) algorithm that uses momentum-based gradient signals over noisy fading MAC to improve the convergence rate as compared to existing methods. Furthermore, AGMA does not require power control or beamforming to cancel the fading effect, which simplifies the implementation complexity. We analyze AGMA theoretically, and establish a finite-sample bound of the error for both convex and strongly convex loss functions with Lipschitz gradient. For the strongly convex case, we show that AGMA approaches the best-known linear convergence rate as the network increases. For the convex case, we show that AGMA significantly improves the sub-linear convergence rate as compared to existing methods. Finally, we present simulation results using real datasets that demonstrate better performance by AGMA.