A common assumption in strategic classification is that the classifier is made public knowledge. However, it remains unclear if, and why, a system would choose to commit to full disclosure. We study a setting in which regulation requires the system to share some, but not all, of the information. This entails a learning task in which the goal is to jointly learn a classifier and the uncertainty surrounding it. Towards this, we adopt from robust mechanism design the notion of ambiguity, which in our setting permits the learner to reveal a set or range of possible classifiers, and choose one to realize. We investigate how ambiguity affects the learning task, propose efficient algorithms for computing best-responses and training, and empirically explore strategic learning and its outcomes in this novel setting and using our approach.
