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Learning sparse combinations is a frequent theme in machine learning. In this paper, we study its associated optimization problem in the distributed setting where the elements to be combined are not centrally located but spread over a network. We address the key challenges of balancing communication costs and optimization errors. To this end, we propose a distributed Frank-Wolfe (dFW) algorithm. We obtain theoretical guarantees on the optimization error ϵ and communication cost that do notarXiv:1404.2644v3 fatcat:5it5qte545gftpflpifrap53ea