We present a novel semi-supervised training algorithm for learning dependency parsers. By combining a supervised large margin loss with an unsupervised least squares loss, a discriminative, convex, semi-supervised learning algorithm can be obtained that is applicable to large-scale problems. To demonstrate the benefits of this approach, we apply the technique to learning dependency parsers from combined labeled and unlabeled corpora. Using a stochastic gradient descent algorithm, a parsing model can be efficiently learned from semi-supervised data that significantly outperforms corresponding supervised methods. .