Uniform Convergence with Square-Root Lipschitz Loss

Part of Advances in Neural Information Processing Systems 36 (NeurIPS 2023) Main Conference Track

Bibtex Paper Supplemental


Lijia Zhou, Zhen Dai, Frederic Koehler, Nati Srebro


We establish generic uniform convergence guarantees for Gaussian data in terms of the Radamacher 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-Lipschtz 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.