Domain-Adjusted Regression or: ERM May Already Learn Features Sufficient for Out-of-Distribution Generalization
This work addresses out-of-distribution generalization for machine learning practitioners, offering a simpler approach that is incremental but practically useful.
The paper challenges the notion that deep networks fail to generalize out-of-distribution due to insufficient feature learning, arguing that ERM already learns sufficient features and the bottleneck is robust regression, with DARE achieving equal or better performance compared to prior methods.
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.