Plug-in Performative Optimization

When predictions are performative, the choice of which predictor to deploy influences the distribution of future observations. The overarching goal in learning under performativity is to find a predictor that has low \emph{performative risk}, that is, good performance on its induced distribution. One family of solutions for optimizing the performative risk, including bandits and other derivative-free methods, is agnostic to any structure in the performative feedback, leading to exceedingly slow convergence rates. A complementary family of solutions makes use of explicit \emph{models} for the feedback, such as best-response models in strategic classification, enabling significantly faster rates. However, these rates critically rely on the feedback model being well-specified. In this work we initiate a study of the use of possibly \emph{misspecified} models in performative prediction. We study a general protocol for making use of models, called \emph{plug-in performative optimization}, and prove bounds on its excess risk. We show that plug-in performative optimization can be far more efficient than model-agnostic strategies, as long as the misspecification is not too extreme. Altogether, our results support the hypothesis that models--even if misspecified--can indeed help with learning in performative settings.