[2603.01719] Co-optimization for Adaptive Conformal Prediction

Statistics > Machine Learning arXiv:2603.01719 (stat) [Submitted on 2 Mar 2026] Title:Co-optimization for Adaptive Conformal Prediction Authors:Xiaoyi Su, Zhixin Zhou, Rui Luo View a PDF of the paper titled Co-optimization for Adaptive Conformal Prediction, by Xiaoyi Su and 2 other authors View PDF HTML (experimental) Abstract:Conformal prediction (CP) provides finite-sample, distribution-free marginal coverage, but standard conformal regression intervals can be inefficient under heteroscedasticity and skewness. In particular, popular constructions such as conformalized quantile regression (CQR) often inherit a fixed notion of center and enforce equal-tailed errors, which can displace the interval away from high-density regions and produce unnecessarily wide sets. We propose Co-optimization for Adaptive Conformal Prediction (CoCP), a framework that learns prediction intervals by jointly optimizing a center $m(x)$ and a radius $h(x)$.CoCP alternates between (i) learning $h(x)$ via quantile regression on the folded absolute residual around the current center, and (ii) refining $m(x)$ with a differentiable soft-coverage objective whose gradients concentrate near the current boundaries, effectively correcting mis-centering without estimating the full conditional density. Finite-sample marginal validity is guaranteed by split-conformal calibration with a normalized nonconformity score. Theory characterizes the population fixed point of the soft objective and shows that, under s...