Wireless Coded Distributed Learning with Gaussian-based Local Differential Privacy

Differentially private distributed machine learning protects privacy by injecting artificial noise to the computing results. To further improve energy efficiency, the natural noise in the wireless environment can be used to protect privacy. In this paper, we study the problem of coded distributed machine learning over Gaussian multiple-access wireless channels to achieve differential privacy by exploiting the natural noise. Firstly, we propose an aggregation scheme using differentially private Lagrange encoding in a wireless environment, where the local computing results are uploaded to the master through orthogonal channels. Then, we develop an achievable privacy protection level to illustrate the impact of transmit power and power allocation on privacy. Additionally, we establish a theoretical convergence upper bound of the proposed scheme, providing a clear understanding of the potential limitations and capabilities of the system. Finally, we demonstrate a trade-off between system resource settings, convergence, and privacy protection levels through experiments. Specifically, increasing the signal-to-noise ratio (SNR) and power allocated for gradient computation leads to a decrease in the privacy protection level of the system and an increase in training accuracy. Moreover, reducing the dataset partitions results in better training accuracy.