  We study the problem of transfer learning, observing that previous efforts to
understand its information-theoretic limits do not fully exploit the geometric
structure of the source and target domains. In contrast, our study first
illustrates the benefits of incorporating a natural geometric structure within
a linear regression model, which corresponds to the generalized eigenvalue
problem formed by the Gram matrices of both domains. We next establish a
finite-sample minimax lower bound, propose a refined model interpolation
estimator that enjoys a matching upper bound, and then extend our framework to
multiple source domains and generalized linear models. Surprisingly, as long as
information is available on the distance between the source and target
parameters, negative-transfer does not occur. Simulation studies show that our
proposed interpolation estimator outperforms state-of-the-art transfer learning
methods in both moderate- and high-dimensional settings.
