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.

翻译：当预测行为具有绩效性时，部署何种预测器的选择会影响未来观测数据的分布。在绩效性学习中的核心目标是找到具有低\emph{绩效风险}的预测器，即在其诱导分布上表现良好的预测器。一类优化绩效风险的解决方案（包括赌博机和其他无导数方法）对绩效反馈中的任何结构都不可知，导致收敛速度极慢。另一类互补性解决方案则利用反馈的显式\emph{模型}（如战略分类中的最优响应模型），从而实现显著更快的收敛速度。然而，这些速度关键依赖于反馈模型的良好设定性。本文首次研究在绩效性预测中使用可能\emph{误设定}模型的问题。我们探究了一种利用模型的通用协议，称为\emph{即插即用绩效优化》，并证明了其超额风险的上界。研究表明，只要误设定程度不太极端，即插即用绩效优化可能比模型不可知策略高效得多。总体而言，我们的结果支持以下假设：即使模型被误设定，也能帮助在绩效性环境中进行学习。