Conformal Prediction at Performative Equilibrium: The Price of Performativity
Abstract
Conformal prediction gives finite-sample coverage when calibration and test points are exchangeable, but exchangeability can fail when deployment changes the data distribution. We study conformal prediction in performative settings, where the deployed predictor affects the data distribution, and seek prediction sets valid at performative equilibrium: coverage must hold under D(f⋆) for a performatively stable predictor f⋆. Under total-variation L-sensitivity of the distribution map, we prove a phase transition at L=1. If L ≥ 1, no finite-sample procedure can uniformly guarantee both equilibrium-valid coverage and nontrivial prediction sets. If L<1, the minimax excess miscoverage over informative procedures is Ω̃(1/((1−L)√n)), implying a sample-complexity inflation of order 1/(1−L)2 for fixed excess miscoverage. Our main technical tool is a transfer theorem: any procedure returning a predictor within ε of equilibrium yields equilibrium-valid coverage up to an additive Lε term after split-conformal calibration. We instantiate the theorem with two retraining algorithms: a model-free method for discretizable classes and a parametric tail-averaged method that matches the n- and L-dependence of this rate up to logarithmic factors. Experiments, including semi-synthetic credit scoring, demonstrate the predicted threshold behavior and scaling laws.
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BibTeX
@misc{mahrous2026conformal,
title = {{Conformal Prediction at Performative Equilibrium: The Price of Performativity}},
author = {Ahmed Mahrous and Roberto Di Pietro},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05277},
eprint = {2611.05277},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05277},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Conformal Prediction at Performative Equilibrium: The Price of Performativity
AU - Ahmed Mahrous
AU - Roberto Di Pietro
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05277
UR - https://arxiv.org/abs/2611.05277
AB - Conformal prediction gives finite-sample coverage when calibration and test points are exchangeable, but exchangeability can fail when deployment changes the data distribution. We study conformal prediction in performative settings, where the deployed predictor affects the data distribution, and seek prediction sets valid at performative equilibrium: coverage must hold under D(f^⋆) for a performatively stable predictor f^⋆. Under total-variation L-sensitivity of the distribution map, we prove a phase transition at L=1. If L ≥ 1, no finite-sample procedure can uniformly guarantee both equilibrium-valid coverage and nontrivial prediction sets. If L<1, the minimax excess miscoverage over informative procedures is Ω̃(1/((1−L)√n)), implying a sample-complexity inflation of order 1/(1−L)^2 for fixed excess miscoverage. Our main technical tool is a transfer theorem: any procedure returning a predictor within ε of equilibrium yields equilibrium-valid coverage up to an additive Lε term after split-conformal calibration. We instantiate the theorem with two retraining algorithms: a model-free method for discretizable classes and a parametric tail-averaged method that matches the n- and L-dependence of this rate up to logarithmic factors. Experiments, including semi-synthetic credit scoring, demonstrate the predicted threshold behavior and scaling laws.
ER -