Complex loss optimization via dual decomposition

We describe a novel max-margin parameter learning approach for structured prediction problems under certain non-decomposable performance measures. Structured prediction is a common approach in many vision problems. Non-decomposable performance measures are also commonplace. However, efficient general methods for learning parameters against non-decomposable performance measures do not exist. In this paper we develop such a method, based on dual decomposition, that is applicable to a large class of non-decomposable performance measures. We exploit dual decomposition to factorize the original hard problem into two smaller problems and show how to optimize each factor efficiently. We show experimentally that the proposed approach significantly outperforms alternatives, which either sacrifice the model structure or approximate the performance measure, and is an order of magnitude faster than a previous approach with comparable results.