  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.
