Section: New Results

Block-Coordinate Frank-Wolfe Optimization for Structural SVMs

Participants : Simon Lacoste-Julien [correspondent] , Mark Schmidt.

Collaboration with: Martin Jaggi (Centre de Mathématiques Appliquées, Ecole Polytechnique), Patrick Pletscher (Machine Learning Laboratory, ETH Zurich).

In [16] we propose a randomized block-coordinate variant of the classic Frank-Wolfe algorithm for convex optimization with block-separable constraints. Despite its lower iteration cost, we show that it achieves a similar convergence rate in duality gap as the full Frank-Wolfe algorithm. We also show that, when applied to the dual structural support vector machine (SVM) objective, it yields an online algorithm that has the same low iteration complexity as primal stochastic subgradient methods. However, unlike stochastic subgradient methods, the block-coordinate Frank-Wolfe algorithm allows us to compute the optimal step-size and yields a computable duality gap guarantee. Our experiments indicate that this simple algorithm outperforms competing structural SVM solvers.