# Uniform Convergence with Square-Root Lipschitz Loss

arXiv: https://arxiv.org/abs/2306.13188 · HTML: https://mlsanity.com/paper/2306.13188/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jun 2023.

## Built on by (most cited first, 2 of 2)

- [Optimistic Rates for Learning from Label Proportions](https://mlsanity.com/paper/2406.00487/) (2024)
- [A Novel Gaussian Min-Max Theorem and its Applications](https://mlsanity.com/paper/2402.07356/) (2024)

## Abstract (arXiv)

We establish generic uniform convergence guarantees for Gaussian data in terms of the Rademacher complexity of the hypothesis class and the Lipschitz constant of the square root of the scalar loss function. We show how these guarantees substantially generalize previous results based on smoothness (Lipschitz constant of the derivative), and allow us to handle the broader class of square-root-Lipschitz losses, which includes also non-smooth loss functions appropriate for studying phase retrieval and ReLU regression, as well as rederive and better understand "optimistic rate" and interpolation learning guarantees.