  This paper studies Dictionary Learning problems wherein the learning task is
distributed over a multi-agent network, modeled as a time-varying directed
graph. This formulation is relevant, for instance, in Big Data scenarios where
massive amounts of data are collected/stored in different locations (e.g.,
sensors, clouds) and aggregating and/or processing all data in a fusion center
might be inefficient or unfeasible, due to resource limitations, communication
overheads or privacy issues. We develop a unified decentralized algorithmic
framework for this class of nonconvex problems, which is proved to converge to
stationary solutions at a sublinear rate. The new method hinges on Successive
Convex Approximation techniques, coupled with a decentralized tracking
mechanism aiming at locally estimating the gradient of the smooth part of the
sum-utility. To the best of our knowledge, this is the first provably
convergent decentralized algorithm for Dictionary Learning and, more generally,
bi-convex problems over (time-varying) (di)graphs.
