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We formalize performative prediction under selective label observation, demonstrating that standard repeated risk minimization (RRM) can diverge from stable solutions due to biased retraining data. To address this, we introduce a worst-case objective using confidence intervals on label probabilities, which, when optimized with RRM, guarantees convergence to a point within a bounded distance of the true stable solution. Experiments in a lending context with fairness constraints validate that this robust optimization approach achieves performance comparable to RRM with full label access.
Retraining on observed data in performative prediction can lead to unstable models, but a worst-case objective with label confidence intervals ensures convergence.
Many social applications of machine learning exhibit performative effects: population behavior changes in response to deployed models. Performative prediction studies this interaction through a distribution map that relates each model to the population distribution it induces. One of the main results in this framework showed that repeated risk minimization (RRM), which updates models by retraining on the most recent data, can converge to a stable model that minimizes risk on its own induced distribution. However, existing analyses typically assume access to the complete distributions of features and labels after model deployment, ignoring the possibility of selective labels: observing labels only for the accepted subset of the population. In this work, we formalize performative prediction with selective labels and show that retraining only on observed data can misguide the retraining procedure and undermine the guarantees of convergence to a stable solution. We then propose a worst-case objective based on knowledge of a confidence interval on the probability of a positive label. Applying RRM to this objective permits us to remain within a bounded distance to the true stable point. Under a sensitivity assumption on the conditional label distribution, we further show how previously accepted data can tighten these confidence intervals over time. Experiments in a lending application with fairness regularization show that our robust optimization approach closely matches the performance of RRM with complete label access.
