Plug-in Performative Optimization

TL;DR

This paper introduces plug-in performative optimization, a method that leverages possibly misspecified models to improve learning efficiency in performative prediction, outperforming model-agnostic approaches when model errors are moderate.

Contribution

It proposes a general protocol for using potentially inaccurate models in performative prediction, demonstrating their potential to enhance learning rates over model-agnostic methods.

Findings

Plug-in approach can outperform model-agnostic strategies with moderate misspecification.

Misspecified models still provide significant benefits in performative learning.

Results support the usefulness of models even when they are not perfectly accurate.

Abstract

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.