Wasserstein Distributionally Robust Performative Prediction

Performativity means that the deployment of a predictive model incentivizes agents to strategically adapt their behavior, thereby inducing a model-dependent distribution shift. Practitioners often repeatedly retrain the model on data samples to adapt to evolving distributions. In this paper, we develop a Wasserstein distributionally robust optimization framework for performative prediction, where the prediction model is optimized over the worst-case distribution within a Wasserstein ambiguity set. We allow the ambiguity radius to depend on the prediction model, which subsumes the constant-radius formulation as a special case. By leveraging strong duality, the intractable robust objective is reformulated as a computationally tractable minimization problem. Based on this formulation, we develop distributionally robust repeated risk minimization (DR-RRM) and repeated gradient descent (DR-RGD), to iteratively find an equilibrium between distributional shifts and model retraining. Theoretical analyses demonstrate that, under standard regularity conditions, both algorithms converge to a unique robust performative stable point. Our analysis explicitly accounts for inner-loop approximation errors and shows convergence to a neighborhood of the stable point in inexact settings. Additionally, we establish theoretical bounds on the suboptimality gap between the stable point and the global performative optimum. Finally, numerical simulations of a dynamic credit scoring problem demonstrate the efficacy of the method.

💡 Research Summary

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The paper tackles the emerging problem of performative prediction, where the deployment of a machine‑learning model influences the data‑generating process, causing a feedback loop between the model parameters and the observed distribution. Traditional performative prediction assumes access to the true induced distribution (P(\theta)), which is rarely observable in practice; instead, only a finite sample from an empirical distribution (\hat P(\theta)) is available. To address this uncertainty, the authors propose a Wasserstein distributionally robust optimization (DRO) framework that minimizes the worst‑case expected loss over a Wasserstein ambiguity set centered at (\hat P(\theta)).

A key novelty is that the ambiguity radius (\rho(\theta)) is allowed to depend on the decision variable (\theta). This decision‑dependent radius subsumes the constant‑radius case and enables the robustness level to shrink as the model stabilizes, thereby avoiding excessive conservatism. The original DRO problem

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