Understanding Why Generalized Reweighting Does Not Improve Over ERM

TL;DR

This paper investigates why generalized reweighting methods do not outperform empirical risk minimization in handling distributional shifts, revealing that under certain conditions they produce similar models to ERM and are thus ineffective for robust generalization.

Contribution

The paper provides a theoretical analysis showing that broad classes of generalized reweighting algorithms yield models similar to ERM, explaining their limited effectiveness in distributional robustness.

Findings

GRW algorithms produce models close to ERM in overparameterized settings

Adding small regularization does not significantly improve robustness

GRW approaches are fundamentally limited in achieving distributionally robust generalization

Abstract

Empirical risk minimization (ERM) is known in practice to be non-robust to distributional shift where the training and the test distributions are different. A suite of approaches, such as importance weighting, and variants of distributionally robust optimization (DRO), have been proposed to solve this problem. But a line of recent work has empirically shown that these approaches do not significantly improve over ERM in real applications with distribution shift. The goal of this work is to obtain a comprehensive theoretical understanding of this intriguing phenomenon. We first posit the class of Generalized Reweighting (GRW) algorithms, as a broad category of approaches that iteratively update model parameters based on iterative reweighting of the training samples. We show that when overparameterized models are trained under GRW, the resulting models are close to that obtained by ERM. We also show that adding small regularization which does not greatly affect the empirical training accuracy does not help. Together, our results show that a broad category of what we term GRW approaches are not able to achieve distributionally robust generalization. Our work thus has the following sobering takeaway: to make progress towards distributionally robust generalization, we either have to develop non-GRW approaches, or perhaps devise novel classification/regression loss functions that are adapted to the class of GRW approaches.