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：绩效预测由Perdomo等人（2020）提出，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部署而发生变化。现有关于优化该场景下准确性的工作依赖于两个在实践中容易被违反的假设：绩效风险在已部署模型上是凸的，并且从模型到数据分布的映射事先为模型设计者所知。本文中，我们首次研究了不依赖这些假设的可处理绩效预测问题。为应对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，另一层将绩效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，并实现可证明的遗憾保证。特别地，我们给出了一个遗憾界，该界限在所用绩效样本总数上呈次线性，且仅与模型参数的维度成多项式关系。