We present a framework for improving task-oriented dialog systems through online interactive teaching with human trainers. A dialog policy trained with imitation learning on a limited corpus may not generalize well to novel dialog flows often uncovered in live interactions. This issue is magnified in multi-action dialog policies which have a more expressive action space. In our approach, a pre-trained dialog policy model interacts with human trainers, and at each turn the trainers choose the best output among N-best multi-action outputs. We present a novel multi-domain, multi-action dialog policy architecture trained on MultiWOZ, and show that small amounts of online supervision can lead to significant improvement in model performance. We also present transfer learning results which show that interactive learning in one domain improves policy model performance in related domains.