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

arXiv: https://arxiv.org/abs/1712.07495 · HTML: https://mlsanity.com/paper/1712.07495/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Dec 2017.

## Built on by (most cited first, 4 of 4)

- [One Gradient Frank-Wolfe for Decentralized Online Convex and Submodular Optimization](https://mlsanity.com/paper/2210.16790/) (2022)
- [Scalable Projection-Free Optimization](https://mlsanity.com/paper/2105.03527/) (2021)
- [Scalable High-Dimensional Multivariate Linear Regression for Feature-Distributed Data](https://mlsanity.com/paper/2307.03410/) (2023)
- [Federated Frank-Wolfe Algorithm](https://mlsanity.com/paper/2408.10090/) (2024)

## Abstract (arXiv)

We consider the problem of learning a high-dimensional but low-rank matrix from a large-scale dataset distributed over several machines, where low-rankness is enforced by a convex trace norm constraint. We propose DFW-Trace, a distributed Frank-Wolfe algorithm which leverages the low-rank structure of its updates to achieve efficiency in time, memory and communication usage. The step at the heart of DFW-Trace is solved approximately using a distributed version of the power method. We provide a theoretical analysis of the convergence of DFW-Trace, showing that we can ensure sublinear convergence in expectation to an optimal solution with few power iterations per epoch. We implement DFW-Trace in the Apache Spark distributed programming framework and validate the usefulness of our approach on synthetic and real data, including the ImageNet dataset with high-dimensional features extracted from a deep neural network.