Performative prediction, as introduced by Perdomo et al. (2020), is a framework for studying social prediction in which the data distribution itself changes in response to the deployment of a model. Existing work on optimizing accuracy in this setting hinges on two assumptions that are easily violated in practice: that the performative risk is convex over the deployed model, and that the mapping from the model to the data distribution is known to the model designer in advance. In this paper, we initiate the study of tractable performative prediction problems that do not require these assumptions. To tackle this more challenging setting, we develop a two-level zeroth-order optimization algorithm, where one level aims to compute the distribution map, and the other level reparameterizes the performative prediction objective as a function of the induced data distribution. Under mild conditions, this reparameterization allows us to transform the non-convex objective into a convex one and achieve provable regret guarantees. In particular, we provide a regret bound that is sublinear in the total number of performative samples taken and only polynomial in the dimension of the model parameter.

翻译：表演性预测（Perdomo et al., 2020）是一个研究社会预测的框架，其中数据分布本身会随着模型的部署而发生改变。现有关于在此情境下优化准确性的工作依赖于两个在实践中容易违反的假设：表演性风险关于所部署模型是凸的，且从模型到数据分布的映射被模型设计者事先知晓。在本文中，我们开创性地研究不依赖这些假设的可解表演性预测问题。为处理这一更具挑战性的场景，我们开发了一种双层零阶优化算法，其中一层旨在计算分布映射，另一层则将表演性预测目标重参数化为诱导数据分布的函数。在温和条件下，这种重参数化使我们能够将非凸目标转化为凸目标，并获得可证明的遗憾保证。特别地，我们给出的遗憾界关于总表演性样本数量是次线性的，且仅关于模型参数维度呈多项式增长。