Solution path algorithm for distributionally robust regression

Abstract

In this paper, we propose a general distributionally robust regression model based on distributionally robust optimization theory. The proposed model has a piecewise linear loss function and elastic net penalty term, and it generalizes many other regression models. We prove the piecewise linear property of the optimal solutions to this model, which enables us to develop a solution path algorithm for the hyperparameter tuning. A Doubly regularized Least Absolute Deviations (DrLAD) regression model is proposed based on this framework, and a solution path algorithm is developed to speed up the tuning of two hyperparameters in this model. Numerical experiments are implemented to validate the performance of this model and the computational efficiency of the solution path algorithm.