Machine learning models have traditionally been developed under the assumption that the training and test distributions match exactly. However, recent success in few-shot learning and related problems are encouraging signs that these models can be adapted to more realistic settings where train and test differ. Unfortunately, there is severely limited theoretical support for these algorithms and little is known about the difficulty of these problems. In this work, we provide novel information-theoretic lower-bounds on minimax rates of convergence for algorithms which are trained on data from multiple sources and tested on novel data. Our bounds depend intuitively on the information shared between sources of data and characterizes the difficulty of learning in this setting for arbitrary algorithms.