Decentralized Dictionary Learning Over Time-Varying Digraphs
This work solves the problem of distributed data processing for big data scenarios, such as in sensor networks, by providing the first provably convergent decentralized algorithm for dictionary learning, though it is incremental in extending existing techniques to this specific domain.
The paper tackles decentralized dictionary learning over time-varying directed graphs by developing a unified algorithmic framework that converges to stationary solutions at a sublinear rate, addressing inefficiencies in data aggregation due to resource and privacy constraints.
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.