  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.
