I will present a formal framework for transfer learning and investigate under which conditions is it possible to provide performance guarantees for such scenarios. I will address two key issues:

• 1) Which notions of task-similarity suffice to provide meaningful error bounds on a target task, for a predictor trained on a (different) source task?
• 2) Can we do better than just train a hypothesis on the source task and analyze its performance on the target task? Can the use of unlabeled target samples reduce the target prediction error?