Optimal Classification under Performative Distribution Shift

Performative learning addresses the increasingly pervasive situations in which algorithmic decisions may induce changes in the data distribution as a consequence of their public deployment. We propose a novel view in which these performative effects are modelled as push forward measures. This general framework encompasses existing models and enables novel performative gradient estimation methods, leading to more efficient and scalable learning strategies. For distribution shifts, unlike previous models which require full specification of the data distribution, we only assume knowledge of the shift operator that represents the performative changes. This approach can also be integrated into various change-of-variable-based models, such as VAEs or normalizing flows.