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We consider the problem of learning a high-dimensional but low-rank matrixfrom a large-scale dataset distributed over several machines, wherelow-rankness is enforced by a convex trace norm constraint. We proposeDFW-Trace, a distributed Frank-Wolfe algorithm which leverages the low-rankstructure of its updates to achieve efficiency in time, memory andcommunication usage. The step at the heart of DFW-Trace is solved approximatelyusing a distributed version of the power method. We provide a theoreticalanalysis of the convergence of DFW-Trace, showing that we can ensure sublinearconvergence in expectation to an optimal solution with few power iterations perepoch. We implement DFW-Trace in the Apache Spark distributed programmingframework and validate the usefulness of our approach on synthetic and realdata, including the ImageNet dataset with high-dimensional features extractedfrom a deep neural network.

A Distributed Frank-Wolfe Framework for Learning Low-Rank Matrices with the Trace Norm