Robust model fitting is a core algorithm in a large number of computer vision applications. Solving this problem efficiently for datasets highly contaminated with outliers is, however, still challenging due to the underlying computational complexity. Recent literature has focused on learning-based algorithms. However, most approaches are supervised which require a large amount of labelled training data. In this paper, we introduce a novel unsupervised learning framework that learns to directly solve robust model fitting. Unlike other methods, our work is agnostic to the underlying input features, and can be easily generalized to a wide variety of LP-type problems with quasi-convex residuals. We empirically show that our method outperforms existing unsupervised learning approaches, and achieves competitive results compared to traditional methods on several important computer vision problems.