We present a unified view of two state-of-the- art non-projective dependency parsers, both approximate: the loopy belief propagation parser of Smith and Eisner (2008) and the re- laxed linear program of Martins et al. (2009). By representing the model assumptions with a factor graph, we shed light on the optimiza- tion problems tackled in each method. We also propose a new aggressive online algorithm to learn the model parameters, which makes use of the underlying variational representation. The algorithm does not require a learning rate parameter and provides a single framework for a wide family of convex loss functions, includ- ing CRFs and structured SVMs. Experiments show state-of-the-art performance for 14 lan- guages.