Patrick Pletscher

Simon Lacoste-Julien, Martin Jaggi, Mark Schmidt et al.

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, this 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.

Patrick Pletscher, Sharon Wulff

MAP inference for general energy functions remains a challenging problem. While most efforts are channeled towards improving the linear programming (LP) based relaxation, this work is motivated by the quadratic programming (QP) relaxation. We propose a novel MAP relaxation that penalizes the Kullback-Leibler divergence between the LP pairwise auxiliary variables, and QP equivalent terms given by the product of the unaries. We develop two efficient algorithms based on variants of this relaxation. The algorithms minimize the non-convex objective using belief propagation and dual decomposition as building blocks. Experiments on synthetic and real-world data show that the solutions returned by our algorithms substantially improve over the LP relaxation.