A Universal Growth Rate for Learning with Smooth Surrogate Losses

arXiv:2405.05968v1 Announce Type: new
Abstract: This paper presents a comprehensive analysis of the growth rate of $H$-consistency bounds (and excess error bounds) for various surrogate losses used in classification. We prove a square-root growth rate near zero for smooth margin-based surrogate losses in binary classification, providing both upper and lower bounds under mild assumptions. This result also translates to excess error bounds. Our lower bound requires weaker conditions than those in previous work for excess error bounds, and our upper …

abstract analysis arxiv binary classification cs.lg error growth losses near paper prove rate square stat.ml type universal