Preserving Privacy in Distributed LASSO

In this paper, we extend the Soft-Thresholding with Exact Line search Algorithm (STELA) to solve the LASSO problem in a fully decentralized manner, where each agent solves its local minimization problem, and cooperates only with its neighbors to update the local solution. Moreover, the privacy of the local data is maintained during the communication of agents via the privacy-preserving average consensus (PPAC) approach which avoids revealing local information from other agents as well as potential eavesdroppers. We examine the proposed algorithm with synthetic data. Simulation results show that with a similar privacy level, the proposed algorithm has a faster convergence speed and better accuracy compared to the stateof-the-art privacy-preserving Primal-Dual Method of Multipliers (p-PDMM) algorithm.