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We study a fundamental transfer learning process from source to target linearregression tasks, including overparameterized settings where there are morelearned parameters than data samples. The target task learning is addressed byusing its training data together with the parameters previously computed forthe source task. We define a transfer learning approach to the target task as alinear regression optimization with a regularization on the distance betweenthe to-be-learned target parameters and the already-learned source parameters.We analytically characterize the generalization performance of our transferlearning approach and demonstrate its ability to resolve the peak ingeneralization errors in double descent phenomena of the minimum L2-normsolution to linear regression. Moreover, we show that for sufficiently relatedtasks, the optimally tuned transfer learning approach can outperform theoptimally tuned ridge regression method, even when the true parameter vectorconforms to an isotropic Gaussian prior distribution. Namely, we demonstratethat transfer learning can beat the minimum mean square error (MMSE) solutionof the independent target task. Our results emphasize the ability of transferlearning to extend the solution space to the target task and, by that, to havean improved MMSE solution. We formulate the linear MMSE solution to ourtransfer learning setting and point out its key differences from the commondesign philosophy to transfer learning.

The Common Intuition to Transfer Learning Can Win or Lose: Case Studies for Linear Regression