当部署影响数据分布：Conformal Prediction 在执行均衡下的覆盖保证研究
Conformal Prediction at Performative Equilibrium: The Price of Performativity
预测模型一上线就改变用户行为，置信区间还算数吗？这篇论文给出了明确答案和算法，做风险敏感应用的人可以看看。
arXiv 论文研究了 performative 场景下的 conformal prediction，即部署的预测器会改变数据分布本身。论文证明在分布映射的总变差敏感度 L=1 处存在相变：当 L≥1 时，任何有限样本程序都无法同时保证均衡有效覆盖和非平凡的预测集；当 L<1 时，minimax 超额误覆盖率为 Ω(1/((1-L)√n))，意味着样本量需按 1/(1-L)² 膨胀。作者提出一个迁移定理，并给出了两种再训练算法实例，包括模型无关方法和参数化尾部平均方法，在半合成信用评分实验中验证了理论阈值行为。
Conformal Prediction at Performative Equilibrium: The Price of Performativity
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.