Bayesian Strategic Classification

Abstract

In strategic classification, agents modify their features, at a cost, to ideally obtain a positive classification from the learner's classifier. The typical response of the learner is to carefully modify their classifier to be robust to such strategic behavior. When reasoning about agent manipulations, most papers that study strategic classification rely on the following strong assumption: agents fully know the exact parameters of the deployed classifier by the learner. This often is an unrealistic assumption when using complex or proprietary machine learning techniques in real-world prediction tasks. We initiate the study of partial information release by the learner in strategic classification. We move away from the traditional assumption that agents have full knowledge of the classifier. Instead, we consider agents that have a common distributional prior on which classifier the learner is using. The learner in our model can reveal truthful, yet not necessarily complete, information about the deployed classifier to the agents. The learner's goal is to release just enough information about the classifier to maximize accuracy. We show how such partial information release can, counter-intuitively, benefit the learner's accuracy, despite increasing agents' abilities to manipulate. We show that while it is intractable to compute the best response of an agent in the general case, there exist oracle-efficient algorithms that can solve the best response of the agents when the learner's hypothesis class is the class of linear classifiers, or when the agents' cost function satisfies a natural notion of submodularity as we define. We then turn our attention to the learner's optimization problem and provide both positive and negative results on the algorithmic problem of how much information the learner should release about the classifier to maximize their expected accuracy.