  Transfer learning has emerged as a powerful technique for improving the
performance of machine learning models on new domains where labeled training
data may be scarce. In this approach a model trained for a source task, where
plenty of labeled training data is available, is used as a starting point for
training a model on a related target task with only few labeled training data.
Despite recent empirical success of transfer learning approaches, the benefits
and fundamental limits of transfer learning are poorly understood. In this
paper we develop a statistical minimax framework to characterize the
fundamental limits of transfer learning in the context of regression with
linear and one-hidden layer neural network models. Specifically, we derive a
lower-bound for the target generalization error achievable by any algorithm as
a function of the number of labeled source and target data as well as
appropriate notions of similarity between the source and target tasks. Our
lower bound provides new insights into the benefits and limitations of transfer
learning. We further corroborate our theoretical finding with various
experiments.
