  The alternating direction method of multipliers (ADMM) has recently been
recognized as a promising approach for large-scale machine learning models.
However, very few results study ADMM from the aspect of communication costs,
especially jointly with running time. In this letter, we investigate the
communication efficiency and running time of ADMM in solving the consensus
optimization problem over decentralized networks. We first review the effort of
random walk ADMM (W-ADMM), which reduces communication costs at the expense of
running time. To accelerate the convergence speed of W-ADMM, we propose the
parallel random walk ADMM (PW-ADMM) algorithm, where multiple random walks are
active at the same time. Moreover, to further reduce the running time of
PW-ADMM, the intelligent parallel random walk ADMM (IPW-ADMM) algorithm is
proposed through integrating the \textit{Random Walk with Choice} with PW-ADMM.
By numerical results from simulations, we demonstrate that the proposed
algorithms can be both communication efficient and fast in running speed
compared with state-of-the-art methods.
