Optimal Power Control for Over-the-Air Federated Learning with Gradient Compression

Federated Learning (FL) has emerged as a transformative approach in distributed machine learning, enabling the collaborative training of models using decentralized datasets from diverse sources such as mobile edge devices. This paradigm not only enhances data privacy but also significantly reduces the communication burden typically associated with centralized data aggregation. In wireless networks, Over-the-air Federated Learning (OTA-FL) has been developed as a communication-efficient solution, allowing for the simultaneous transmission and aggregation of model updates from numerous edge devices across the available bandwidth. Gradient compression techniques are necessary to further enhance the communication efficiency of FL, particularly in bandwidth-constrained wireless environments. Despite these advancements, OTA-FL with gradient compression encounters substantial challenges, including learning performance degradation due to compression errors, non-uniform channel fading, and noise interference. Existing power control strategies have yet to fully address these issues, leaving a significant gap in optimizing OTA-FL performance under gradient compression. This paper introduces a novel power control strategy that coordinately integrates gradient compression to optimize OTAFL performance by minimizing the impact of channel fading and noise. Our approach employs linear approximations to complex terms, ensuring the stability and effectiveness of each gradient descent iteration. Numerical results demonstrate that our strategy significantly enhances convergence rates compared to traditional methods like channel inversion and uniform power transmission. This research advances the OTA-FL field and opens new avenues for performance tuning in communication-efficient federated learning systems. © 2024 IEEE.