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-variablebased models, such as VAEs or normalizing flows. Focusing on classification with a linear-in-parameters performative effect, we prove the convexity of the performative risk under a new set of assumptions. Notably, we do not limit the strength of performative effects but rather their direction, requiring only that classification becomes harder when deploying more accurate models. In this case, we also establish a connection with adversarially robust classification by reformulating the minimization of the performative risk as a min-max variational problem. Finally, we illustrate our approach on synthetic and real datasets.

翻译：可执行学习致力于解决日益普遍的场景：算法决策在公开部署后可能引发数据分布的变化。我们提出一种新颖视角，将此类可执行效应建模为前推测度。这一通用框架不仅涵盖现有模型，还支持新型可执行梯度估计方法，从而实现更高效、可扩展的学习策略。针对分布偏移问题，与先前需要完整数据分布设定的模型不同，我们仅假设已知表征可执行变化的偏移算子。该方法亦可集成至各类基于变量变换的模型中，例如变分自编码器或标准化流。聚焦于具有线性参数可执行效应的分类问题，我们在新假设集下证明了可执行风险的凸性。值得注意的是，我们并不限制可执行效应的强度，而是约束其方向，仅要求部署更精确模型时分类任务会变得更困难。在此情形下，通过将可执行风险最小化重构为极小-极大变分问题，我们建立了与对抗鲁棒分类的关联。最后，我们在合成与真实数据集上验证了所提方法。