Federated Learning over Wireless Fading Channels (1907.09769v2)

Abstract: We study federated machine learning at the wireless network edge, where limited power wireless devices, each with its own dataset, build a joint model with the help of a remote parameter server (PS). We consider a bandwidth-limited fading multiple access channel (MAC) from the wireless devices to the PS, and propose various techniques to implement distributed stochastic gradient descent (DSGD). We first propose a digital DSGD (D-DSGD) scheme, in which one device is selected opportunistically for transmission at each iteration based on the channel conditions; the scheduled device quantizes its gradient estimate to a finite number of bits imposed by the channel condition, and transmits these bits to the PS in a reliable manner. Next, motivated by the additive nature of the wireless MAC, we propose a novel analog communication scheme, referred to as the compressed analog DSGD (CA-DSGD), where the devices first sparsify their gradient estimates while accumulating error, and project the resultant sparse vector into a low-dimensional vector for bandwidth reduction. Numerical results show that D-DSGD outperforms other digital approaches in the literature; however, in general the proposed CA-DSGD algorithm converges faster than the D-DSGD scheme and other schemes in the literature, and reaches a higher level of accuracy. We have observed that the gap between the analog and digital schemes increases when the datasets of devices are not independent and identically distributed (i.i.d.). Furthermore, the performance of the CA-DSGD scheme is shown to be robust against imperfect channel state information (CSI) at the devices. Overall these results show clear advantages for the proposed analog over-the-air DSGD scheme, which suggests that learning and communication algorithms should be designed jointly to achieve the best end-to-end performance in machine learning applications at the wireless edge.

Federated Learning over Wireless Fading Channels

The paper "Federated Learning over Wireless Fading Channels" by Mohammad Mohammadi Amiri and Deniz Gündüz explores the implementation of federated learning (FL) in a wireless network setting, particularly focusing on constrained communication environments characterized by bandwidth-limited fading multiple access channels (MACs). This paper addresses the joint design of machine learning and communication strategies to efficiently perform distributed stochastic gradient descent (DSGD) at the network edge.

Key Contributions

1. Digital and Analog DSGD Schemes: The paper introduces two novel methods for federated learning over wireless channels: a digital DSGD (D-DSGD) and a compressed analog DSGD (CA-DSGD).

• D-DSGD Scheme: The digital approach schedules one device per iteration based on channel conditions to transmit quantized gradients to a parameter server (PS). This method uses a digital compression technique and ensures reliable transmission by adhering to the available channel capacity.
• CA-DSGD Scheme: The analog approach leverages the additive nature of the wireless channels. Devices sparsify and accumulate errors from past iterations and then apply a random linear projection for dimensionality reduction before analog transmission. This scheme aligns received gradients efficiently while maintaining robustness against noisy channel estimates.

1. Performance Analysis: The authors present numerical evaluations comparing D-DSGD and CA-DSGD with existing methods across various scenarios. Notably, CA-DSGD demonstrates faster convergence and higher final accuracy, especially when datasets are not independent and identically distributed (non-i.i.d.) across devices.
2. Robustness to Channel State Information (CSI): The CA-DSGD is shown to be resilient to imperfect CSI, maintaining performance advantages even when channel knowledge is imprecise. This highlights the applicability of the proposed method in real-world environments with unstable channel conditions.

Implications and Future Directions

• Joint Learning and Communication Design: The research underscores the importance of designing machine learning algorithms that incorporate communication characteristics, which is crucial for efficient utilization of limited wireless resources in FL.
• Scalability and Efficiency: The proposed CA-DSGD technique offers a compelling solution for edge learning, particularly pertinent in scenarios with low-powered IoT devices and severe bandwidth constraints.
• Potential for Privacy Preservation: Moreover, due to inherent aggregation and noise, analog transmission schemes like CA-DSGD could provide additional privacy benefits, a significant aspect for federated learning applications.
• Future Development: The paper paves the way for further exploration into hybrid schemes that may blend digital precision with analog efficiency. It also invites the investigation into adaptive techniques that dynamically choose between digital and analog transmissions based on current network states and learning objectives.

This paper advances the field by providing systematic approaches to overcoming key challenges faced in deploying federated learning over wireless networks, offering both theoretical insights and practical guidelines. The innovative methodologies and sound analysis present a substantive contribution to the field of federated learning and wireless communication.