Data systems often present examples and solicit labels from users to learn a target model, i.e., active learning. However, due to the complexity of the underlying data, users may not initially have a perfect understanding of the effective model and do not know the accurate labeling. For example, a user who is training a model for detecting noisy or abnormal values may not perfectly know the properties of typical and clean values in the data. Users may improve their knowledge about the data and target model as they observe examples during training. As users gradually learn about the data and model, they may revise their labeling strategies. Current systems assume that users always provide correct labeling with potentially a fixed and small chance of annotation mistakes. Nonetheless, if the trainer revises its belief during training, such mistakes become significant and non-stationarity. Hence, current systems consume incorrect labels and may learn inaccurate models. In this paper, we build theoretical underpinnings and design algorithms to develop systems that collaborate with users to learn the target model accurately and efficiently. At the core of our proposal, a game-theoretic framework models the joint learning of user and system to reach a desirable eventual stable state, where both user and system share the same belief about the target model. We extensively evaluate our system using user studies over various real-world datasets and show that our algorithms lead to accurate results with a smaller number of interactions compared to existing methods.