New Algorithm Boosts Robustness in Linear Regression for Group Data

This paper presents a novel algorithmic approach to tackle the group distributionally robust (GDR) least squares problem. The method leverages a geometric construction known as block Lewis weights, linking the empirical GDR problem to a specific least squares formulation, and integrates accelerated proximal methods. The result is an algorithm that can find a solution within a small multiplicative factor of the optimal, outperforming current interior point methods in certain accuracy ranges. The new technique offers significant speed improvements, particularly for scenarios requiring moderate accuracy. It also matches the best-known guarantees for the specialized case of L-infinity regression. Furthermore, the researchers provide algorithms that smoothly transition between minimizing average least squares loss and the more robust distributionally robust loss, offering flexibility for various applications.