Plug-in Performative Optimization
This work addresses the challenge of efficient learning in performative prediction for machine learning practitioners, offering a method that balances model reliance with robustness to misspecification, though it is incremental as it builds on existing model-based solutions.
The paper tackles the problem of optimizing predictors under performative feedback, where predictions influence future data distributions, by proposing a plug-in performative optimization method that leverages possibly misspecified models. The result shows this approach outperforms model-agnostic strategies when model misspecification is moderate, supporting the use of models to improve learning in such settings.
When predictions are performative, the choice of which predictor to deploy influences the distribution of future observations. The overarching goal in learning under performativity is to find a predictor that has low \emph{performative risk}, that is, good performance on its induced distribution. One family of solutions for optimizing the performative risk, including bandits and other derivative-free methods, is agnostic to any structure in the performative feedback, leading to exceedingly slow convergence rates. A complementary family of solutions makes use of explicit \emph{models} for the feedback, such as best-response models in strategic classification, enabling faster rates. However, these rates critically rely on the feedback model being correct. In this work we study a general protocol for making use of possibly misspecified models in performative prediction, called \emph{plug-in performative optimization}. We show this solution can be far superior to model-agnostic strategies, as long as the misspecification is not too extreme. Our results support the hypothesis that models, even if misspecified, can indeed help with learning in performative settings.