Extreme Value Theory (EVT) provides statistical tools to model the behavior of random variables under extreme conditions, typically when the norm of a covariate exceeds a high threshold. In many contexts (covariate-shifts, climate change), it is essential to construct predictors with good extrapolation properties.
Recent works have shown that, under regular variation assumptions, extrapolation can be achieved by learning from the angular components of the most extreme observations. However, these prior analyses have been confined to binary classification or least square regression within an empirical risk minimization framework. In this work, we consider a penalized learning approach, focusing on SVM-based quantile regression. We establish finite-sample learning guarantees and illustrate our results on a real multivariate dataset involving river flow measurement on the Danube river network.