One essential function of dialogue systems is the ability to ask questions and acquire necessary information from the user through dialogue. To avoid degrading user engagement through repetitive questioning, the number of such questions should be kept low. In this study, we cast knowledge acquisition through dialogue as stream-based active learning, exemplified by the segmentation of user utterances containing novel words. In stream-based active learning, data instances are presented sequentially, and the system selects an action for each instance based on an acquisition function that determines whether to request the correct answer from the oracle (in this case, the user). To improve the efficiency of training the acquisition function via reinforcement learning, we introduce two extensions: (1) a new action that performs semi-supervised learning, and (2) a state representation that takes the remaining budget into account. Our simulation-based experiments showed that these two extensions improved word segmentation performance with fewer questions for the user, compared to a baseline without these extensions.