Performative prediction is a framework for learning models that influence the
data they intend to predict. We focus on finding classifiers that are
performatively stable, i.e. optimal for the data distribution they induce.
Standard convergence results for finding a performatively stable classifier
with the method of repeated risk minimization assume that the data distribution
is Lipschitz continuous to the model's parameters. Under this assumption, the
loss must be strongly convex and smooth in these parameters; otherwise, the
method will diverge for some problems. In this work, we instead assume that the
data distribution is Lipschitz continuous with respect to the model's
predictions, a more natural assumption for performative systems. As a result,
we are able to significantly relax the assumptions on the loss function. In
particular, we do not need to assume convexity with respect to the model's
parameters. As an illustration, we introduce a resampling procedure that models
realistic distribution shifts and show that it satisfies our assumptions. We
support our theory by showing that one can learn performatively stable
classifiers with neural networks making predictions about real data that shift
according to our proposed procedure.

该研究提出一种执行预测框架，关注于找到稳定的分类器来影响他们要预测的数据；并且可以放松关于损失函数的假设，通过使用 Lipschitz 连续的预测数据分布。通过实验，该研究表明可以使用这种方法学习关于真实数据的神经网络分类器。