  Theoretical studies on transfer learning or domain adaptation have so far
focused on situations with a known hypothesis class or model; however in
practice, some amount of model selection is usually involved, often appearing
under the umbrella term of hyperparameter-tuning: for example, one may think of
the problem of tuning for the right neural network architecture towards a
target task, while leveraging data from a related source task.
  Now, in addition to the usual tradeoffs on approximation vs estimation errors
involved in model selection, this problem brings in a new complexity term,
namely, the transfer distance between source and target distributions, which is
known to vary with the choice of hypothesis class.
  We present a first study of this problem, focusing on classification; in
particular, the analysis reveals some remarkable phenomena: adaptive rates,
i.e., those achievable with no distributional information, can be arbitrarily
slower than oracle rates, i.e., when given knowledge on distances.
