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

TL;DR

This paper introduces DFW-Trace, a distributed Frank-Wolfe algorithm that efficiently learns low-rank matrices from large-scale, distributed datasets by exploiting trace norm constraints and low-rank structures, with theoretical guarantees and practical validation.

Contribution

The paper presents DFW-Trace, a novel distributed Frank-Wolfe algorithm that leverages low-rank structure for efficient large-scale matrix learning with theoretical convergence analysis.

Findings

Achieves sublinear convergence with few power iterations

Efficient in time, memory, and communication in distributed settings

Validated on synthetic and real datasets including ImageNet

Abstract

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.