Robust high dimensional learning for Lipschitz and convex losses

Understand

We establish risk bounds for Regularized Empirical Risk Minimizers (RERM) when the loss is Lipschitz and convex and the regularization function is a norm.

• In a first part, we obtain these results in the i.i.d.
• setup under subgaussian assumptions on the design.
• In a second part, a more general framework where the design might have heavier tails and data may be corrupted by outliers both in the design and the response variables is considered.