Minding the Gaps for Block Frank-Wolfe Optimization of Structured SVMs

TL;DR

This paper enhances the block-coordinate Frank-Wolfe algorithm for structured SVMs by introducing adaptive sampling, variants, caching, and regularization path computation, leading to improved efficiency and empirical performance.

Contribution

It introduces novel adaptive gap-based sampling, pairwise and away-step variants, caching strategies, and a method for approximate regularization path computation for SSVMs.

Findings

Improved convergence and efficiency demonstrated on four datasets.

Adaptive gap-based sampling outperforms uniform sampling.

New method for computing regularization paths for SSVMs.

Abstract

In this paper, we propose several improvements on the block-coordinate Frank-Wolfe (BCFW) algorithm from Lacoste-Julien et al. (2013) recently used to optimize the structured support vector machine (SSVM) objective in the context of structured prediction, though it has wider applications. The key intuition behind our improvements is that the estimates of block gaps maintained by BCFW reveal the block suboptimality that can be used as an adaptive criterion. First, we sample objects at each iteration of BCFW in an adaptive non-uniform way via gapbased sampling. Second, we incorporate pairwise and away-step variants of Frank-Wolfe into the block-coordinate setting. Third, we cache oracle calls with a cache-hit criterion based on the block gaps. Fourth, we provide the first method to compute an approximate regularization path for SSVM. Finally, we provide an exhaustive empirical evaluation of all our methods on four structured prediction datasets.