A good dialogue agent should have the ability to interact with users by both responding to questions and by asking questions, and importantly to learn from both types of interaction. In this work, we explore this direction by designing a simulator and a set of synthetic tasks in the movie domain that allow such interactions between a learner and a teacher. We investigate how a learner can benefit from asking questions in both offline and online reinforcement learning settings, and demonstrate that the learner improves when asking questions. Finally, real experiments with Mechanical Turk validate the approach. Our work represents a first step in developing such end-to-end learned interactive dialogue agents.