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：当预测具有表现性时，部署预测器的选择会影响未来观测值的分布。在表现性情境下学习的核心目标是找到具有低\textit{表现性风险}的预测器，即在其诱导分布上表现良好。一类优化表现性风险的方法（包括多臂赌博机及其他无导数方法）对表现性反馈中的任何结构都不可知，导致收敛速度极慢。另一类互补方法则利用反馈的显式\textit{模型}（例如策略分类中的最佳响应模型），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正确设定。本文首次研究了在表现性预测中使用可能\textit{误设}模型的问题。我们提出了一种通用的模型利用协议，称为\textit{插件式表现性优化}，并证明了其超额风险的界。结果表明，只要误设程度不太极端，插件式表现性优化可远优于模型不可知策略。总体而言，我们的研究结果支持以下假设：即使模型是误设的，在表现性情境中仍有助于学习。