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 imposed strong restrictions on how models influenced distributions. By using a martingale argument and allowing randomization, we avoid any assumption on how populations respond to predictions and sidestep recent hardness results showing that deterministic stable models are in general PPAD-hard to compute. 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：在决策过程中使用算法预测会导致反馈循环，即我们部署的模型会主动影响随后看到并用于重新训练的数据分布。Perdomo等人（2020）在其关于可执行预测的研究中正式化了这一动态过程。我们的主要结果是一个无条件约简：在可执行环境中部署的任何无遗憾算法都会收敛到（混合）可执行稳定均衡——即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最优。在我们的工作之前，该领域的所有正面结果都对模型如何影响分布施加了严格限制。通过使用鞅论证并允许随机化，我们避免了对群体如何响应预测的任何假设，并绕过了近期表明确定性稳定模型通常为PPAD难计算的困难结果。最后，从更概念性的角度来看，我们的联系揭示了为什么梯度下降等常见算法天然具有稳定性并能阻止失控反馈循环。我们希望我们的工作能够促进在线优化与可执行性之间的未来技术思想迁移。