The use of algorithmic predictions in decision-making leads to a feedback loop where the models we deploy actively influence the data distributions we see, and later use to retrain on. This dynamic was formalized by Perdomo et al. 2020 in their work on performative prediction. Our main result is an unconditional reduction showing that any no-regret algorithm deployed in performative settings converges to a (mixed) performatively stable equilibrium: a solution in which models actively shape data distributions in ways that their own predictions look optimal in hindsight. Prior to our work, all positive results in this area made strong restrictions on how models influenced distributions. By using a martingale argument and allowing randomization, we avoid any such assumption and sidestep recent hardness results for finding stable models. Lastly, on a more conceptual note, our connection sheds light on why common algorithms, like gradient descent, are naturally stabilizing and prevent runaway feedback loops. We hope our work enables future technical transfer of ideas between online optimization and performativity.

翻译：算法预测在决策中的应用导致了一种反馈循环：我们部署的模型会主动影响我们观察到的数据分布，而后我们又利用这些分布进行模型重训练。Perdomo等人（2020）在其关于表演性预测的研究中对这一动态过程进行了形式化描述。我们的主要成果是一个无条件归约证明：任何在表演性场景中部署的无悔算法都会收敛到一个（混合）表演性稳定均衡——在该解中，模型主动塑造数据分布的方式使得其自身的预测在事后看来是最优的。在本研究之前，该领域的所有积极成果都对模型影响分布的方式施加了严格限制。通过采用鞅论证方法并允许随机化，我们避免了任何此类假设，并规避了近期关于寻找稳定模型的困难性结论。最后从概念层面而言，我们的关联性分析揭示了为何常见算法（如梯度下降）天然具有稳定特性并能防止失控的反馈循环。我们希望本研究能为在线优化与表演性理论之间的思想迁移提供未来的技术桥梁。