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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2601.20180 |
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| _version_ | 1866911403909054464 |
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| author | Anagnostides, Ioannis Chauhan, Rohan Panageas, Ioannis Sandholm, Tuomas Yan, Jingming |
| author_facet | Anagnostides, Ioannis Chauhan, Rohan Panageas, Ioannis Sandholm, Tuomas Yan, Jingming |
| contents | 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 ($ρ< 1$), the complexity in the regime $ρ> 1$ was hitherto open. In this paper, we establish a sharp phase transition: computing an $ε$-performatively stable point is PPAD-complete -- and thus polynomial-time equivalent to Nash equilibria in general-sum games -- even when $ρ= 1 + O(ε)$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20180 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Computational Complexity of Performative Prediction Anagnostides, Ioannis Chauhan, Rohan Panageas, Ioannis Sandholm, Tuomas Yan, Jingming Machine Learning 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 ($ρ< 1$), the complexity in the regime $ρ> 1$ was hitherto open. In this paper, we establish a sharp phase transition: computing an $ε$-performatively stable point is PPAD-complete -- and thus polynomial-time equivalent to Nash equilibria in general-sum games -- even when $ρ= 1 + O(ε)$. 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. |
| title | On the Computational Complexity of Performative Prediction |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2601.20180 |