Over-the-Air Federated Learning from Heterogeneous Data (2009.12787v2)

Abstract: Federated learning (FL) is a framework for distributed learning of centralized models. In FL, a set of edge devices train a model using their local data, while repeatedly exchanging their trained updates with a central server. This procedure allows tuning a centralized model in a distributed fashion without having the users share their possibly private data. In this paper, we focus on over-the-air (OTA) FL, which has been suggested recently to reduce the communication overhead of FL due to the repeated transmissions of the model updates by a large number of users over the wireless channel. In OTA FL, all users simultaneously transmit their updates as analog signals over a multiple access channel, and the server receives a superposition of the analog transmitted signals. However, this approach results in the channel noise directly affecting the optimization procedure, which may degrade the accuracy of the trained model. We develop a Convergent OTA FL (COTAF) algorithm which enhances the common local stochastic gradient descent (SGD) FL algorithm, introducing precoding at the users and scaling at the server, which gradually mitigates the effect of the noise. We analyze the convergence of COTAF to the loss minimizing model and quantify the effect of a statistically heterogeneous setup, i.e. when the training data of each user obeys a different distribution. Our analysis reveals the ability of COTAF to achieve a convergence rate similar to that achievable over error-free channels. Our simulations demonstrate the improved convergence of COTAF over vanilla OTA local SGD for training using non-synthetic datasets. Furthermore, we numerically show that the precoding induced by COTAF notably improves the convergence rate and the accuracy of models trained via OTA FL.

Overview of "Over-the-Air Federated Learning from Heterogeneous Data"

This paper presents a novel approach to Federated Learning (FL) called Convergent Over-the-Air Federated Learning (COTAF), which addresses a significant challenge in FL: reducing communication overhead while allowing efficient model training using diverse datasets from multiple users. The focus is on utilizing over-the-air (OTA) computation to aggregate model updates over a shared wireless multiple access channel without the typical constraints of orthogonal transmission schemes.

Contributions

1. OTA Federated Learning: The paper proposes using OTA computation, where analog signals representing model updates are transmitted simultaneously by users over a shared channel. This approach allows high throughput communication, as users utilize the full bandwidth without dividing channel resources. Unlike traditional methods that treat the channel as bit-limited and error-free, OTA transmission leverages the natural aggregation property of the wireless channel.
2. Noise Mitigation and Precoding: A key innovation in COTAF is the introduction of precoding at users and dynamic scaling at the server. These techniques aim to control the impact of channel noise, which can severely degrade learning accuracy. Precoding adjusts the power of transmitted updates based on statistical properties of the gradients, while server-side scaling transforms the received signal to approximate a noiseless sum.
3. Convergence Analysis: The authors provide a rigorous convergence analysis showing that COTAF achieves a convergence rate comparable to FL with noise-free channels, even in statistically heterogeneous environments. This is shown through theoretical bounds that illustrate how noise-induced errors can be controlled over time.
4. Experimental Validation: The effectiveness of COTAF is demonstrated through simulations involving non-synthetic datasets, such as the Million Song Dataset and CIFAR-10 for image classification tasks using convolutional neural networks. Results indicate that COTAF not only improves convergence speed but can achieve performance close to centralized training without data sharing.

Implications and Future Directions

The implications of this research are multifaceted, impacting both theoretical and practical domains:

• Practical Implementation: COTAF eliminates the need for complex orthogonalization in wireless communication, offering a scalable solution for deploying FL in real-world scenarios where high throughput and minimal latency are critical.
• Theoretical Extensions: The convergence analysis opens avenues for exploring OTA aggregation under different channel conditions and system parameters, potentially extending to fading channels and adaptive transmission schemes.
• AI Developments: As FL gains traction in privacy-preserving AI applications, robust methods like COTAF can enable efficient model training across diverse devices and environments, contributing to the broader development of distributed AI systems.

Overall, this paper provides a comprehensive exploration of how OTA computation can transform federated learning by effectively managing communication overhead and ensuring convergence in challenging conditions. Future work may explore further integration with adaptive communication protocols and refinement of precoding techniques to enhance performance in dynamic and diverse network setups.