Uniform Convergence with Square-Root Lipschitz Loss

Lijia Zhou, Zhen Dai, Frederic Koehler, Nathan Srebro

Keywords: Uniform Convergence, Square-Root Lipschitz, Benign Overfitting, Minimal Norm Interpolation, Phase Retrieval, ReLU Regression, Matrix Sensing

Abstract: 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.

Submission Number: 10458