Surrogate regret bounds for proper losses

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.

• Type: Conference
• Year: 2009
• Where: ICML
• Authors: Mark D. Reid, Robert C. Williamson
• Keywords: Composite Losses, ICML 2009, Machine Learning, Proper Losses, Surrogate Regret Bounds