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In performative prediction, predictions guide decision-making and hence caninfluence the distribution of future data. To date, work on performativeprediction has focused on finding performatively stable models, which are thefixed points of repeated retraining. However, stable solutions can be far fromoptimal when evaluated in terms of the performative risk, the loss experiencedby the decision maker when deploying a model. In this paper, we shift attentionbeyond performative stability and focus on optimizing the performative riskdirectly. We identify a natural set of properties of the loss function andmodel-induced distribution shift under which the performative risk is convex, aproperty which does not follow from convexity of the loss alone. Furthermore,we develop algorithms that leverage our structural assumptions to optimize theperformative risk with better sample efficiency than generic methods forderivative-free convex optimization.

Outside the Echo Chamber: Optimizing the Performative Risk