Surrogate Regret Bounds for Proper Losses
Mark Reid and Bob Williamson
In: ICML 2009, Montreal(2009).
We present tight surrogate regret bounds for the
class of proper (i.e., Fisher consistent) losses.
The bounds generalise the margin-based bounds
due to Bartlett et al. (2006). The proof uses Taylor’s
theorem and leads to new representations
for loss and regret and a simple proof of the integral
representation of proper losses. We also
present a different formulation of a duality result
of Bregman divergences which leads to a simple
demonstration of the convexity of composite
losses using canonical link functions