People are becoming increasingly comfortable using Digital Assistants (DAs) to interact with services or connected objects. However, for non-programming users, the available possibilities for customizing their DA are limited and do not include the possibility of teaching the assistant new tasks. To make the most of the potential of DAs, users should be able to customize assistants by instructing them through Natural Language (NL). To provide such functionalities, NL interpretation in traditional assistants should be improved: (1) The intent identification system should be able to recognize new forms of known intents, and to acquire new intents as they are expressed by the user. (2) In order to be adaptive to novel intents, the Natural Language Understanding module should be sample efficient, and should not rely on a pretrained model. Rather, the system should continuously collect the training data as it learns new intents from the user. In this work, we propose AidMe (Adaptive Intent Detection in Multi-Domain Environments), a user-in-the-loop adaptive intent detection framework that allows the assistant to adapt to its user by learning his intents as their interaction progresses. AidMe builds its repertoire of intents and collects data to train a model of semantic similarity evaluation that can discriminate between the learned intents and autonomously discover new forms of known intents. AidMe addresses two major issues - intent learning and user adaptation - for instructable digital assistants. We demonstrate the capabilities of AidMe as a standalone system by comparing it with a one-shot learning system and a pretrained NLU module through simulations of interactions with a user. We also show how AidMe can smoothly integrate to an existing instructable digital assistant.