Semi-Stochastic Frank-Wolfe Algorithms with Away-Steps for Block-Coordinate Structure Problems

TL;DR

This paper introduces semi-stochastic Frank-Wolfe algorithms with away-steps for block-structured problems, demonstrating linear convergence and superior performance in machine learning applications like SVMs and fused LASSO.

Contribution

It develops novel semi-stochastic Frank-Wolfe algorithms with away-steps for block-coordinate problems, extending their applicability and proving linear convergence in expectation.

Findings

Algorithms converge linearly in expectation.

Outperform competing methods in iteration cost.

Effective on problems like SVMs and fused LASSO.

Abstract

We propose a semi-stochastic Frank-Wolfe algorithm with away-steps for regularized empirical risk minimization and extend it to problems with block-coordinate structure. Our algorithms use adaptive step-size and we show that they converge linearly in expectation. The proposed algorithms can be applied to many important problems in statistics and machine learning including regularized generalized linear models, support vector machines and many others. In preliminary numerical tests on structural SVM and graph-guided fused LASSO, our algorithms outperform other competing algorithms in both iteration cost and total number of data passes.