Conformal Prediction at Performative Equilibrium: The Price of Performativity
Ahmed Mahrous, Roberto Di Pietro
AI 速览：研究部署预测器会改变数据分布时，保形预测在表演性均衡处能否保持覆盖有效性，并揭示敏感度 L=1 处的相变与样本复杂度膨胀。
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 $D(f^\star)$ for a performatively stable predictor $f^\star$. Under total-variation $L$-sensitivity of the distribution map, we prove a phase transition at $L=1$. If $L \ge 1$, 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 $\widetildeΩ(1/((1-L)\sqrt{n}))$, 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 $\varepsilon$ of equilibrium yields equilibrium-valid coverage up to an additive $L\varepsilon$ 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.
Using a near-census of 802,863 resolved markets listed on Polymarket between January 2023 and May 2026, and only information available at listing (the market's title and description, named resolution source, and contract metadata), we predict lifetime trading volume and whether settlement is later disputed. Contract information predicts trading volume well (out-of-sample $R^2 = 0.747$ for log volume), and most of the signal is interpretable: market topic provides the largest gain ($+0.289$ $R^2$ over a $0.220$ contract-feature baseline), wording and resolution-rule design add smaller but measurable improvements ($+0.027$ combined), and neural text models add little beyond the interpretable features. This performance does not survive a period of platform change coinciding with a shift in listing formats: accuracy in predicting whether a market reaches \$1,000 falls from AUC $0.940$ under same-period evaluation to $0.577$ when training on past quarters and testing on later ones. The loss concentrates in markets whose question forms were absent from training (76.9% of test markets; on familiar forms the model still reaches $0.778$), and a decomposition attributes more of it to a changed relationship between contract characteristics and demand than to an outdated mapping from text to features. Dispute predictors are more stable but less precise: launch-time features rank dispute risk far better than chance (AUC $0.78$), yet at a 0.31% base rate precision is too low for case-by-case prediction (average precision $0.012$), so the scores suit ranking groups of markets rather than forecasting individual disputes.