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On Analog Gradient Descent Learning over Multiple Access Fading Channels

arXiv 1908.07463 ↗First posted 20 Aug 2019cs.LG cs.IT math.ITcited by 61

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Abstract (arXiv)

We consider a distributed learning problem over multiple access channel (MAC) using a large wireless network. The computation is made by the network edge and is based on received data from a large number of distributed nodes which transmit over a noisy fading MAC. The objective function is a sum of the nodes' local loss functions. This problem has attracted a growing interest in distributed sensing systems, and more recently in federated learning. We develop a novel Gradient-Based Multiple Access (GBMA) algorithm to solve the distributed learning problem over MAC. Specifically, the nodes transmit an analog function of the local gradient using common shaping waveforms and the network edge receives a superposition of the analog transmitted signals used for updating the estimate. GBMA does not require power control or beamforming to cancel the fading effect as in other algorithms, and operates directly with noisy distorted gradients. We analyze the performance of GBMA theoretically, and prove that it can approach the convergence rate of the centralized gradient descent (GD) algorithm in large networks. Specifically, we establish a finite-sample bound of the error for both convex and strongly convex loss functions with Lipschitz gradient. Furthermore, we provide energy scaling laws for approaching the centralized convergence rate as the number of nodes increases. Finally, experimental results support the theoretical findings, and demonstrate strong performance of GBMA using synthetic and real data.

Key facts. Cited by 61 papers in the map (data through 7 Oct 2026). First posted on arXiv 20 Aug 2019.

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Citing papers per year: 2021: 16; 2022: 9; 2023: 15; 2024: 11; 2025: 5; 2026: 5.

61 papers.

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  19. 2021Federated Learning with Downlink Device Selectioncited by 3
  20. 2021Learning, Computing, and Trustworthiness in Intelligent IoT Environments: Performance-Energy Tradeoffscited by 3
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  23. 2024Robust Federated Learning Over the Air: Combating Heavy-Tailed Noise with Median Anchored Clippingcited by 3
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  25. 2021Adaptive Scheduling for Machine Learning Tasks over Networkscited by 2
  26. 2021Fundamental limits of over-the-air optimization: Are analog schemes optimal?cited by 2
  27. 2022Over-The-Air Federated Learning Over Scalable Cell-free Massive MIMOcited by 2
  28. 2023Sparse Training for Federated Learning with Regularized Error Correctioncited by 2
  29. 2021Over-the-Air Federated Learning with Retransmissions (Extended Version)cited by 1
  30. 2022Matching Pursuit Based Scheduling for Over-the-Air Federated Learningcited by 1
  31. 2023Accelerating Wireless Federated Learning via Nesterov's Momentum and Distributed Principle Component Analysiscited by 1
  32. 2023Differentially Private Wireless Federated Learning Using Orthogonal Sequencescited by 1
  33. 2024GP-FL: Model-Based Hessian Estimation for Second-Order Over-the-Air Federated Learningcited by 1
  34. 2025PAUSE: Low-Latency and Privacy-Aware Active User Selection for Federated Learningcited by 1
  35. 2025Rethinking Federated Learning Over the Air: The Blessing of Scaling Upcited by 1
  36. 2026Age-Aware Edge-Blind Federated Learning via Over-the-Air Aggregationcited by 1
  37. 2022Random Orthogonalization for Federated Learning in Massive MIMO Systemscited by 0
  38. 2023Semi-Asynchronous Federated Edge Learning Mechanism via Over-the-air Computationcited by 0

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