Title: On Structured Prediction Theory with Calibrated Convex Surrogate Losses,
Abstract: We provide novel theoretical insights on structured prediction in the context
of efficient convex surrogate loss minimization with consistency guarantees.
For any task loss, we construct a convex surrogate that can be optimized via
stochastic gradient descent and we prove tight bounds on the so-called
"calibration function" relating the excess surrogate risk to the actual risk.
In contrast to prior related work, we carefully monitor the effect of the
exponential number of classes in the learning guarantees as well as on the
optimization complexity. As an interesting consequence, we formalize the
intuition that some task losses make learning harder than others, and that the
classical 0-1 loss is ill-suited for general structured prediction.