We propose an interactive approach to language learning that utilizes linguistic acceptability judgments from an informant (a competent language user) to learn a grammar. Given a grammar formalism and a framework for synthesizing data, our model iteratively selects or synthesizes a data-point according to one of a range of information-theoretic policies, asks the informant for a binary judgment, and updates its own parameters in preparation for the next query. We demonstrate the effectiveness of our model in the domain of phonotactics, the rules governing what kinds of sound-sequences are acceptable in a language, and carry out two experiments, one with typologically-natural linguistic data and another with a range of procedurally-generated languages. We find that the information-theoretic policies that our model uses to select items to query the informant achieve sample efficiency comparable to, and sometimes greater than, fully supervised approaches.