To date, work on performative prediction has only focused on unconstrained scenarios, neglecting the fact that many real-world learning problems are subject to constraints.

Performative prediction characterizes environments where predictive models alter the very data distributions they aim to forecast, triggering complex feedback loops. While prior research treats single-agent and multi-agent performativity as distinct phenomena, this paper introduces a unified statistical inference framework that bridges these contexts, treating the former as a special case of the latter. Our contribution is two-fold. First, we put forward the Repeated Risk Minimization (RRM) procedure for estimating the performative stability, and establish a rigorous inferential theory for admitting its asymptotic normality and confirming its asymptotic efficiency. Second, for the performative optimality, we introduce a novel two-step plug-in estimator that integrates the idea of Recalibrated Prediction Powered Inference (RePPI) with Importance Sampling, and further provide formal derivations for the Central Limit Theorems of both the underlying distributional parameters and the plug-in results. The theoretical analysis demonstrates that our estimator achieves the semiparametric efficiency bound and maintains robustness under mild distributional misspecification. This work provides a principled toolkit for reliable estimation and decision-making in dynamic, performative environments.

Performative prediction aims to model scenarios where predictive outcomes subsequently influence the very systems they target. The pursuit of a performative optimum (PO)--minimizing performative risk--is generally reliant on modeling of the distribution map, which characterizes how a deployed ML model alters the data distribution. Unfortunately, inevitable misspecification of the distribution map can lead to a poor approximation of the true PO. To address this issue, we introduce a novel framework of distributionally robust performative prediction and study a new solution concept termed as distributionally robust performative optimum (DRPO). We show provable guarantees for DRPO as a robust approximation to the true PO when the nominal distribution map is different from the actual one. Moreover, distributionally robust performative prediction can be reformulated as an augmented performative prediction problem, enabling efficient optimization. The experimental results demonstrate that DRPO offers potential advantages over traditional PO approach when the distribution map is misspecified at either micro-or macro-level.

Performative prediction aims to model scenarios where predictive outcomes subsequently influence the very systems they target.

To date, work on performative prediction has only focused on unconstrained scenarios, neglecting the fact that many real-world learning problems are subject to constraints.

What sets this setting apart from traditional stochastic optimization is the difference between merely updating model parameters and deploying the new model.

Performative Prediction addresses scenarios where deploying a model induces a distribution shift in the input data, such as individuals modifying their features and reapplying for a bank loan after rejection. Literature has had a theoretical perspective giving mathematical guarantees for convergence (either to the stable or optimal point). We believe that visualization of the loss landscape can complement this theoretical advances with practical insights. Therefore, (1) we introduce a simple decoupled risk visualization method inspired in the two-step process that performative prediction is. Our approach visualizes the risk landscape with respect to two parameter vectors: model parameters and data parameters. We use this method to propose new properties of the interest points, to examine how existing algorithms traverse the risk landscape and perform under more realistic conditions, including strategic classification with non-linear models. (2) Building on this decoupled risk visualization, we introduce a novel setting - extended Performative Prediction - which captures scenarios where the distribution reacts to a model different from the decision-making one, reflecting the reality that agents often lack full access to the deployed model.

Performative prediction aims to model scenarios where predictive outcomes subsequently influence the very systems they target. The pursuit of a performative optimum (PO)--minimizing performative risk--is generally reliant on modeling of the distribution map, which characterizes how a deployed ML model alters the data distribution. Unfortunately, inevitable misspecification of the distribution map can lead to a poor approximation of the true PO. To address this issue, we introduce a novel framework of distributionally robust performative prediction and study a new solution concept termed as distributionally robust performative optimum (DRPO). We show provable guarantees for DRPO as a robust approximation to the true PO when the nominal distribution map is different from the actual one.