Similarity and distance functions are essential to many learning algorithms, thus training them has attracted a lot of interest. When it comes to dealing with structured data (e.g., strings or trees), edit similarities are widely used, and there exists a few methods for learning them. However, these methods offer no theoretical guarantee as to the generalization performance and discriminative power of the resulting similarities. Recently, a theory of learning with (ε, γ, τ)-good similarity functions was proposed. This new theory bridges the gap between the properties of a similarity function and its performance in classification. In this paper, we propose a novel edit similarity learning approach (GESL) driven by the idea of (ε, γ, τ)-goodness, which allows us to derive generalization guarantees using the notion of uniform stability. We experimentally show that edit similarities learned with our method induce classification models that are both more accurate and sparser than those induced by the edit distance or edit similarities learned with a state-of-the-art method.