Multi-consensus decentralized primal-dual fixed point algorithm for distributed learning

Decentralized distributed learning has recently attracted significant attention in many applications in machine learning and signal processing. To solve a decentralized optimization with regularization, we propose a Multi-consensus Decentralized Primal-Dual Fixed Point (MD-PDFP) algorithm. We apply multiple consensus steps with the gradient tracking technique to extend the primal-dual fixed point method over a network. The communication complexities of our procedure are given under certain conditions. Moreover, we show that our algorithm is consistent under general conditions and enjoys global linear convergence under strong convexity. With some particular choices of regularizations, our algorithm can be applied to decentralized machine learning applications. Finally, several numerical experiments and real data analyses are conducted to demonstrate the effectiveness of the proposed algorithm.