# Boosting with the Logistic Loss is Consistent

arXiv: https://arxiv.org/abs/1305.2648 · HTML: https://mlsanity.com/paper/1305.2648/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 May 2013.

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

- [Early-stopped neural networks are consistent](https://mlsanity.com/paper/2106.05932/) (2021)
- [Boosting with Tempered Exponential Measures](https://mlsanity.com/paper/2306.05487/) (2023)
- [Smoothly Giving up: Robustness for Simple Models](https://mlsanity.com/paper/2302.09114/) (2023)

## Abstract (arXiv)

This manuscript provides optimization guarantees, generalization bounds, and statistical consistency results for AdaBoost variants which replace the exponential loss with the logistic and similar losses (specifically, twice differentiable convex losses which are Lipschitz and tend to zero on one side). The heart of the analysis is to show that, in lieu of explicit regularization and constraints, the structure of the problem is fairly rigidly controlled by the source distribution itself. The first control of this type is in the separable case, where a distribution-dependent relaxed weak learning rate induces speedy convergence with high probability over any sample. Otherwise, in the nonseparable case, the convex surrogate risk itself exhibits distribution-dependent levels of curvature, and consequently the algorithm's output has small norm with high probability.