Outside the Echo Chamber: Optimizing the Performative Risk
This work addresses the challenge for decision-makers in dynamic environments where model predictions affect outcomes, offering a more optimal approach than previous stability-focused methods, though it is incremental in advancing the field of performative prediction.
The paper tackles the problem of optimizing the performative risk directly in performative prediction, where predictions influence future data distributions, moving beyond stable models to achieve better performance. It shows that under certain conditions, the performative risk is convex and develops algorithms with improved sample efficiency, such as achieving a convergence rate of O(1/√T) in some cases.
In performative prediction, predictions guide decision-making and hence can influence the distribution of future data. To date, work on performative prediction has focused on finding performatively stable models, which are the fixed points of repeated retraining. However, stable solutions can be far from optimal when evaluated in terms of the performative risk, the loss experienced by the decision maker when deploying a model. In this paper, we shift attention beyond performative stability and focus on optimizing the performative risk directly. We identify a natural set of properties of the loss function and model-induced distribution shift under which the performative risk is convex, a property which does not follow from convexity of the loss alone. Furthermore, we develop algorithms that leverage our structural assumptions to optimize the performative risk with better sample efficiency than generic methods for derivative-free convex optimization.