D-FW: Communication efficient distributed algorithms for high-dimensional sparse optimization

We propose distributed algorithms for high-dimensional sparse optimization. In many applications, the parameter is sparse but high-dimensional. This is pathological for existing distributed algorithms as the latter require an information exchange stage involving transmission of the full parameter, which may not be sparse during the intermediate steps of optimization. The novelty of this work is to develop communication efficient algorithms using the stochastic Frank-Wolfe (sFW) algorithm, where the gradient computation is inexact but controllable. For star network topology, we propose an algorithm with low communication cost and establishes its convergence. The proposed algorithm is then extended to perform decentralized optimization on general network topology. Numerical experiments are conducted to verify our findings.