This work considers the relationship between convex surrogate loss and learning problem such as classification and ranking. The authors prove that this approach is equivalent, in a strong sense, to working with polyhedral (piecewise linear convex) losses, and give a construction of a link function through which L is a consistent surrogate for the loss it embeds. Some examples are presented to verify the theoretical analysis. This is an interesting direction in learning theory, while I have some concerns as follows: 1) What's the motivation of polyhedral losses? The authors should present some real applications and shows its importance, especially for some new learning problems and settings.