Transfer Learning Can Outperform the True Prior in Double Descent Regularization

We study a fundamental transfer learning process from source to target linear regression tasks, including overparameterized settings where there are more learned parameters than data samples. The target task learning is addressed by using its training data together with the parameters previously computed for the source task. We define the target task as a linear regression optimization with a regularization on the distance between the to-be-learned target parameters and the already-learned source parameters. This approach can be also interpreted as adjusting the previously learned source parameters for the purpose of the target task, and in the case of sufficiently related tasks this process can be perceived as fine tuning. We analytically characterize the generalization performance of our transfer learning approach and demonstrate its ability to resolve the peak in generalization errors in double descent phenomena of min-norm solutions to ordinary least squares regression. Moreover, we show that for sufficiently related tasks the optimally tuned transfer learning approach can outperform the optimally tuned ridge regression method, even when the true parameter vector conforms with isotropic Gaussian prior distribution. Namely, we demonstrate that transfer learning can beat the minimum mean square error (MMSE) solution of the individual target task.