题目：Online Individualized Treatment Selection under Partial Feedback: False Discovery Control and Assignment Regret

摘要：Across diverse applications, individualized treatment policies aim to match treatments to individual needs, but unsuccessful treatment can impose substantial costs or burdens on recipients. We study sequential treatment assignment and online learning of a policy that maximizes treatment coverage while limiting the expected failure proportion among recipients. Because only assigned outcomes are observed, a policy that relies solely on current predictions may fail to collect sufficient data to evaluate alternative assignments. We propose the Partial Feedback Adaptive Individualized Treatment Selection (PAITS) procedure, which balances implementing the learned recommendation rule with randomized exploration to improve future assignments. PAITS calibrates its selection threshold using treatment outcomes evaluated against an estimated covariate-specific control reference. Under regularity conditions, our theory establishes joint guarantees for reliable decision-making and efficient learning: PAITS asymptotically controls the false discovery rate, approaches oracle treatment coverage, and incurs sublinear gap-weighted assignment regret. We further quantify the assignment cost of nuisance estimation under prescribed uniform accuracy requirements. Suitably tuned PAITS attains the corresponding constrained nonparametric minimax regret rate up to logarithmic factors. The effectiveness of error control and efficiency of treatment assignments under PAITS are evaluated through simulations and a Jester replay study.