Decentralized Dictionary Learning Over Time-Varying Digraphs
Abstract
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.
Cite
@article{arxiv.1808.05933,
title = {Decentralized Dictionary Learning Over Time-Varying Digraphs},
author = {Amir Daneshmand and Ying Sun and Gesualdo Scutari and Francisco Facchinei and Brian M. Sadler},
journal= {arXiv preprint arXiv:1808.05933},
year = {2019}
}