Wasserstein Distributionally Robust Performative Prediction
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910014274273280 |
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| author | Wang, Siyi Wang, Zifan Johansson, Karl H. |
| author_facet | Wang, Siyi Wang, Zifan Johansson, Karl H. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06730 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Wasserstein Distributionally Robust Performative Prediction Wang, Siyi Wang, Zifan Johansson, Karl H. Optimization and Control 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. |
| title | Wasserstein Distributionally Robust Performative Prediction |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2602.06730 |