Domain-Adjusted Regression or: ERM May Already Learn Features Sufficient for Out-of-Distribution Generalization

TL;DR

This paper challenges the idea that deep networks fail out-of-distribution generalization due to feature learning issues, showing that robust regression on existing features can suffice, and introduces DARE, a method for domain-adjusted prediction.

Contribution

The paper demonstrates that ERM learns sufficient features for out-of-distribution generalization and introduces DARE, a convex method for robust domain-adjusted regression with theoretical guarantees.

Findings

ERM learns sufficient features for OOD generalization.

DARE outperforms prior methods on finetuned features.

DARE has provable minimax optimality and convergence guarantees.

Abstract

A common explanation for the failure of deep networks to generalize out-of-distribution is that they fail to recover the "correct" features. We challenge this notion with a simple experiment which suggests that ERM already learns sufficient features and that the current bottleneck is not feature learning, but robust regression. Our findings also imply that given a small amount of data from the target distribution, retraining only the last linear layer will give excellent performance. We therefore argue that devising simpler methods for learning predictors on existing features is a promising direction for future research. Towards this end, we introduce Domain-Adjusted Regression (DARE), a convex objective for learning a linear predictor that is provably robust under a new model of distribution shift. Rather than learning one function, DARE performs a domain-specific adjustment to unify the domains in a canonical latent space and learns to predict in this space. Under a natural model, we prove that the DARE solution is the minimax-optimal predictor for a constrained set of test distributions. Further, we provide the first finite-environment convergence guarantee to the minimax risk, improving over existing analyses which only yield minimax predictors after an environment threshold. Evaluated on finetuned features, we find that DARE compares favorably to prior methods, consistently achieving equal or better performance.