Understanding Why Generalized Reweighting Does Not Improve Over ERMDownload PDF

Published: 01 Feb 2023, Last Modified: 01 Oct 2023ICLR 2023 posterReaders: Everyone
Keywords: Distribution shift, Subpopulation shift, Implicit bias, Generalization, Overparameterization
TL;DR: We theoretically prove that the broad family of GRW algorithms which covers many popular methods has an implicit bias almost equivalent to ERM, and thus cannot improve over ERM.
Abstract: Empirical risk minimization (ERM) is known to be non-robust in practice 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 GRW approaches.
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