# Decentralized Dictionary Learning Over Time-Varying Digraphs

arXiv: https://arxiv.org/abs/1808.05933 · HTML: https://mlsanity.com/paper/1808.05933/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Aug 2018.

## Built on by (most cited first, 3 of 3)

- [A Decentralized Adaptive Momentum Method for Solving a Class of Min-Max Optimization Problems](https://mlsanity.com/paper/2106.06075/) (2021)
- [Decentralized Weakly Convex Optimization Over the Stiefel Manifold](https://mlsanity.com/paper/2303.17779/) (2023)
- [Decentralized Complete Dictionary Learning via ℓ4-Norm Maximization](https://mlsanity.com/paper/2211.03628/) (2022)

## Abstract (arXiv)

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.