# On the Rates of Convergence from Surrogate Risk Minimizers to the Bayes Optimal Classifier

arXiv: https://arxiv.org/abs/1802.03688 · HTML: https://mlsanity.com/paper/1802.03688/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2018.

## Built on by (most cited first, 3 of 3)

- [A Universal Growth Rate for Learning with Smooth Surrogate Losses](https://mlsanity.com/paper/2405.05968/) (2024)
- [Surrogate Regret Bounds for Polyhedral Losses](https://mlsanity.com/paper/2110.14031/) (2021)
- [Establishing Linear Surrogate Regret Bounds for Convex Smooth Losses via Convolutional Fenchel-Young Losses](https://mlsanity.com/paper/2505.09432/) (2025)

## Abstract (arXiv)

We study the rates of convergence from empirical surrogate risk minimizers to the Bayes optimal classifier. Specifically, we introduce the notion of consistency intensity to characterize a surrogate loss function and exploit this notion to obtain the rate of convergence from an empirical surrogate risk minimizer to the Bayes optimal classifier, enabling fair comparisons of the excess risks of different surrogate risk minimizers. The main result of the paper has practical implications including (1) showing that hinge loss is superior to logistic and exponential loss in the sense that its empirical minimizer converges faster to the Bayes optimal classifier and (2) guiding to modify surrogate loss functions to accelerate the convergence to the Bayes optimal classifier.