COINS: Any-Stage-Valid and Utility-Oriented Sequential Conformal Prediction

RESUMO

Many predictive workflows update uncertainty as information is acquired and use intermediate reports to determine whether to stop or deploy further resources. We study conformal inference in this setting, treating the resulting prediction sequence as the inferential object. We require any-stage validity, which protects against miscoverage at any inspected stage, and use process-level utility to evaluate how efficiently the sequence supports downstream action. We propose a universal structural theory for constructing any-stage valid prediction sequences. Guided by it, we develop COINS, which coordinates calibration across stages by investing a common finite-sample rejection-count budget only among surviving augmented observations. Under exchangeability, COINS achieves finite-sample any-stage validity and produces prediction sets no larger than their matched Bonferroni counterparts at every stage. We further develop Vopt-COINS, which learns the stagewise allocation for a specified process-level utility, together with branchwise and localized extensions for heterogeneous acquisition pathways and test units. Simulations and a dermatological-diagnosis application confirm any-stage validity and demonstrate gains over Bonferroni and fixed allocations. The proposed methods also perform favorably in ordered score aggregation, viewed as a terminal-utility special case.