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Structural support vector machines (SSVMs) are amongst the best performingmodels for structured computer vision tasks, such as semantic imagesegmentation or human pose estimation. Training SSVMs, however, iscomputationally costly, because it requires repeated calls to a structuredprediction subroutine (called \emph{max-oracle}), which has to solve anoptimization problem itself, e.g. a graph cut.  In this work, we introduce a new algorithm for SSVM training that is moreefficient than earlier techniques when the max-oracle is computationallyexpensive, as it is frequently the case in computer vision tasks. The main ideais to (i) combine the recent stochastic Block-Coordinate Frank-Wolfe algorithmwith efficient hyperplane caching, and (ii) use an automatic selection rule fordeciding whether to call the exact max-oracle or to rely on an approximate onebased on the cached hyperplanes.  We show experimentally that this strategy leads to faster convergence to theoptimum with respect to the number of requires oracle calls, and that thistranslates into faster convergence with respect to the total runtime when themax-oracle is slow compared to the other steps of the algorithm.  A publicly available C++ implementation is provided athttp://pub.ist.ac.at/~vnk/papers/SVM.html .

A Multi-Plane Block-Coordinate Frank-Wolfe Algorithm for Training Structural SVMs with a Costly max-Oracle