Linear-Core Surrogates: Smooth Loss Functions with Linear Rates for Classification and Structured Prediction
A fundamental dichotomy in the theory of classification sets smoothness against statistical efficiency: smooth surrogate losses such as the logistic loss enable fast $O(1/T)$ optimization but yield slow square-root $H$-consistency bounds, while piecewise-linear losses like the Hinge loss achieve optimal linear $H$-consistency rates but are non-differentiable. We introduce Linear-Core (LC) Surrogates, the first family of explicit convex loss functions that provably resolve this tension. By stitching a linear core to a smooth tail, we construct surrogates that are differentiable everywhere ($C^1$, and even $C^2$ under mild conditions) while retaining strict linear $H$-consistency bounds, th...
| Authors | Mehryar Mohri, Yutao Zhong |
|---|---|
| Primary category | cs.LG |
| Published | 30 April 2026 |
| Last updated at source | 11 August 2026 |
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