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