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arXiv · 2601.20180

On the Computational Complexity of Performative Prediction

Ioannis Anagnostides·Rohan Chauhan·Ioannis Panageas·Tuomas Sandholm·Jingming Yan
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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.

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Ioannis Anagnostides, Rohan Chauhan, Ioannis Panageas, Tuomas Sandholm, Jingming Yan. 2026-01-28. On the Computational Complexity of Performative Prediction. https://arxiv.org/abs/2601.20180

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