Performative Prediction in a Stateful World

Deployed supervised machine learning models make predictions that interact with and influence the world. This phenomenon is called "performative prediction" by Perdomo et al. (2020), who investigated it in a stateless setting. We generalize their results to the case where the response of the population to the deployed classifier depends both on the classifier and the previous distribution of the population. We also demonstrate such a setting empirically, for the scenario of strategic manipulation.