# Over-the-Air Federated Learning via Second-Order Optimization

arXiv: https://arxiv.org/abs/2203.15488 · HTML: https://mlsanity.com/paper/2203.15488/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 66 references that are in the map.
- First posted on arXiv 29 Mar 2022.

## Builds on (most cited first, 30 of 42)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Towards Federated Learning at Scale: System Design](https://mlsanity.com/paper/1902.01046/) (2019)
- [signSGD: Compressed Optimisation for Non-Convex Problems](https://mlsanity.com/paper/1802.04434/) (2018)
- [Federated Optimization: Distributed Machine Learning for On-Device Intelligence](https://mlsanity.com/paper/1610.02527/) (2016)
- [A Field Guide to Federated Optimization](https://mlsanity.com/paper/2107.06917/) (2021)
- [Sketching as a Tool for Numerical Linear Algebra](https://mlsanity.com/paper/1411.4357/) (2014)
- [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)
- [PowerSGD: Practical Low-Rank Gradient Compression for Distributed Optimization](https://mlsanity.com/paper/1905.13727/) (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)
- [The Roadmap to 6G -- AI Empowered Wireless Networks](https://mlsanity.com/paper/1904.11686/) (2019)
- [Is Local SGD Better than Minibatch SGD?](https://mlsanity.com/paper/2002.07839/) (2020)
- [Communication Efficient Distributed Optimization using an Approximate Newton-type Method](https://mlsanity.com/paper/1312.7853/) (2013)
- [One-Bit Over-the-Air Aggregation for Communication-Efficient Federated Edge Learning: Design and Convergence Analysis](https://mlsanity.com/paper/2001.05713/) (2020)
- [FedSplit: An algorithmic framework for fast federated optimization](https://mlsanity.com/paper/2005.05238/) (2020)
- [Communication-Efficient Edge AI: Algorithms and Systems](https://mlsanity.com/paper/2002.09668/) (2020)
- [Federated Accelerated Stochastic Gradient Descent](https://mlsanity.com/paper/2006.08950/) (2020)
- [ZO-AdaMM: Zeroth-Order Adaptive Momentum Method for Black-Box Optimization](https://mlsanity.com/paper/1910.06513/) (2019)
- [CoCoA: A General Framework for Communication-Efficient Distributed Optimization](https://mlsanity.com/paper/1611.02189/) (2016)
- [Privacy For Free: Wireless Federated Learning Via Uncoded Transmission With Adaptive Power Control](https://mlsanity.com/paper/2006.05459/) (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)
- [Optimized Power Control Design for Over-the-Air Federated Edge Learning](https://mlsanity.com/paper/2106.09316/) (2021)
- [GIANT: Globally Improved Approximate Newton Method for Distributed Optimization](https://mlsanity.com/paper/1709.03528/) (2017)
- [Federated Learning via Intelligent Reflecting Surface](https://mlsanity.com/paper/2011.05051/) (2020)
- [Reconfigurable Intelligent Surface Enabled Federated Learning: A Unified Communication-Learning Design Approach](https://mlsanity.com/paper/2011.10282/) (2020)
- [Learning Rate Optimization for Federated Learning Exploiting Over-the-air Computation](https://mlsanity.com/paper/2102.02946/) (2021)
- [Harnessing Wireless Channels for Scalable and Privacy-Preserving Federated Learning](https://mlsanity.com/paper/2007.01790/) (2020)

## Built on by (most cited first, 11 of 11)

- [FedSpeed: Larger Local Interval, Less Communication Round, and Higher Generalization Accuracy](https://mlsanity.com/paper/2302.10429/) (2023)
- [Over-the-Air Federated Learning and Optimization](https://mlsanity.com/paper/2310.10089/) (2023)
- [Joint Age-based Client Selection and Resource Allocation for Communication-Efficient Federated Learning over NOMA Networks](https://mlsanity.com/paper/2304.08996/) (2023)
- [Blind Federated Learning via Over-the-Air q-QAM](https://mlsanity.com/paper/2311.04253/) (2023)
- [Adaptive Federated Learning Over the Air](https://mlsanity.com/paper/2403.06528/) (2024)
- [Over-the-Air Fair Federated Learning via Multi-Objective Optimization](https://mlsanity.com/paper/2501.03392/) (2025)
- [Heterogeneity-aware Personalized Federated Learning via Adaptive Dual-Agent Reinforcement Learning](https://mlsanity.com/paper/2501.16966/) (2025)
- [GP-FL: Model-Based Hessian Estimation for Second-Order Over-the-Air Federated Learning](https://mlsanity.com/paper/2412.03867/) (2024)
- [Federated Linear Bandit Learning via Over-the-Air Computation](https://mlsanity.com/paper/2308.13298/) (2023)
- [Accelerated Training of Federated Learning via Second-Order Methods](https://mlsanity.com/paper/2505.23588/) (2025)
- [AirGC-CD: Gaussian-Circulant Precoding for Exactly Debiasable PAPR Reduction in Over-the-Air Federated Learning](https://mlsanity.com/paper/2609.23084/) (2026)

## Abstract (arXiv)

Federated learning (FL) is a promising learning paradigm that can tackle the increasingly prominent isolated data islands problem while keeping users' data locally with privacy and security guarantees. However, FL could result in task-oriented data traffic flows over wireless networks with limited radio resources. To design communication-efficient FL, most of the existing studies employ the first-order federated optimization approach that has a slow convergence rate. This however results in excessive communication rounds for local model updates between the edge devices and edge server. To address this issue, in this paper, we instead propose a novel over-the-air second-order federated optimization algorithm to simultaneously reduce the communication rounds and enable low-latency global model aggregation. This is achieved by exploiting the waveform superposition property of a multi-access channel to implement the distributed second-order optimization algorithm over wireless networks. The convergence behavior of the proposed algorithm is further characterized, which reveals a linear-quadratic convergence rate with an accumulative error term in each iteration. We thus propose a system optimization approach to minimize the accumulated error gap by joint device selection and beamforming design. Numerical results demonstrate the system and communication efficiency compared with the state-of-the-art approaches.