  Transfer learning is essential when sufficient data comes from the source
domain, with scarce labeled data from the target domain. We develop estimators
that achieve minimax linear risk for linear regression problems under
distribution shift. Our algorithms cover different transfer learning settings
including covariate shift and model shift. We also consider when data are
generated from either linear or general nonlinear models. We show that linear
minimax estimators are within an absolute constant of the minimax risk even
among nonlinear estimators for various source/target distributions.
