论文标题
表演预测的随机优化
Stochastic Optimization for Performative Prediction
论文作者
论文摘要
在表演性预测中，模型的选择通常通过基于模型的预测采取的动作来影响未来数据的分布。 我们启动对表演预测的随机优化研究。设置此设置与传统随机优化不同的是，仅更新模型参数和部署新模型之间的区别。后者触发了影响未来数据的分布的转变，而前者则保持分布原样。 假设平稳性和强大的凸度，我们证明了每次随机更新（贪婪地部署）以及在重新部署之前进行多个更新（懒惰部署）之前的贪婪部署模型的收敛速率。在这两种情况下，随着性能的强度降低，我们的边界平稳地恢复了最佳$ O（1/K）$。此外，它们说明了如何取决于表演效应的强度，存在一种方法，即两种方法的表现都超过了另一个。我们通过实验探索合成数据和战略分类模拟器的权衡。
In performative prediction, the choice of a model influences the distribution of future data, typically through actions taken based on the model's predictions. We initiate the study of stochastic optimization for performative prediction. What sets this setting apart from traditional stochastic optimization is the difference between merely updating model parameters and deploying the new model. The latter triggers a shift in the distribution that affects future data, while the former keeps the distribution as is. Assuming smoothness and strong convexity, we prove rates of convergence for both greedily deploying models after each stochastic update (greedy deploy) as well as for taking several updates before redeploying (lazy deploy). In both cases, our bounds smoothly recover the optimal $O(1/k)$ rate as the strength of performativity decreases. Furthermore, they illustrate how depending on the strength of performative effects, there exists a regime where either approach outperforms the other. We experimentally explore the trade-off on both synthetic data and a strategic classification simulator.
