On the Computational Complexity of Performative Prediction

Ioannis Anagnostides, Rohan Chauhan, Ioannis Panageas, Tuomas Sandholm, Jingming Yan
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:2552-2576, 2026.

Abstract

Performative prediction captures the phenomenon where deploying a predictive model shifts the underlying data distribution. While simple retraining dynamics are known to converge linearly when the performative effects are weak ($\rho < 1$), the complexity in the regime $\rho > 1$ was hitherto open. In this paper, we establish a sharp phase transition: computing an $\epsilon$-performatively stable point is PPAD-complete—and thus polynomial-time equivalent to Nash equilibria in general-sum games—even when $\rho = 1 + O(\epsilon)$. This intractability persists even in the ostensibly simple setting with a quadratic loss function and linear distribution shifts. One of our key technical contributions is to extend this PPAD-hardness result to general convex domains, which is of broader interest in the complexity of variational inequalities. Finally, we address the special case of strategic classification, showing that computing a strategic local optimum is PLS-hard.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-anagnostides26a, title = {On the Computational Complexity of Performative Prediction}, author = {Anagnostides, Ioannis and Chauhan, Rohan and Panageas, Ioannis and Sandholm, Tuomas and Yan, Jingming}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {2552--2576}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/anagnostides26a/anagnostides26a.pdf}, url = {https://proceedings.mlr.press/v306/anagnostides26a.html}, abstract = {Performative prediction captures the phenomenon where deploying a predictive model shifts the underlying data distribution. While simple retraining dynamics are known to converge linearly when the performative effects are weak ($\rho < 1$), the complexity in the regime $\rho > 1$ was hitherto open. In this paper, we establish a sharp phase transition: computing an $\epsilon$-performatively stable point is PPAD-complete—and thus polynomial-time equivalent to Nash equilibria in general-sum games—even when $\rho = 1 + O(\epsilon)$. This intractability persists even in the ostensibly simple setting with a quadratic loss function and linear distribution shifts. One of our key technical contributions is to extend this PPAD-hardness result to general convex domains, which is of broader interest in the complexity of variational inequalities. Finally, we address the special case of strategic classification, showing that computing a strategic local optimum is PLS-hard.} }
Endnote
%0 Conference Paper %T On the Computational Complexity of Performative Prediction %A Ioannis Anagnostides %A Rohan Chauhan %A Ioannis Panageas %A Tuomas Sandholm %A Jingming Yan %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-anagnostides26a %I PMLR %P 2552--2576 %U https://proceedings.mlr.press/v306/anagnostides26a.html %V 306 %X Performative prediction captures the phenomenon where deploying a predictive model shifts the underlying data distribution. While simple retraining dynamics are known to converge linearly when the performative effects are weak ($\rho < 1$), the complexity in the regime $\rho > 1$ was hitherto open. In this paper, we establish a sharp phase transition: computing an $\epsilon$-performatively stable point is PPAD-complete—and thus polynomial-time equivalent to Nash equilibria in general-sum games—even when $\rho = 1 + O(\epsilon)$. This intractability persists even in the ostensibly simple setting with a quadratic loss function and linear distribution shifts. One of our key technical contributions is to extend this PPAD-hardness result to general convex domains, which is of broader interest in the complexity of variational inequalities. Finally, we address the special case of strategic classification, showing that computing a strategic local optimum is PLS-hard.
APA
Anagnostides, I., Chauhan, R., Panageas, I., Sandholm, T. & Yan, J.. (2026). On the Computational Complexity of Performative Prediction. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:2552-2576 Available from https://proceedings.mlr.press/v306/anagnostides26a.html.

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