Feedback-Enhanced Online Multiple Testing with Applications to Conformal Selection

• URL: http://arxiv.org/abs/2509.03297v1
• Date: Wed, 03 Sep 2025 13:24:06 GMT
• Title: Feedback-Enhanced Online Multiple Testing with Applications to Conformal Selection
• Authors: Lin Lu, Yuyang Huo, Haojie Ren, Zhaojun Wang, Changliang Zou,
• Abstract summary: We study online multiple testing with feedback, where decisions are made sequentially and the true state of the hypothesis is revealed after the decision has been made.<n>We propose GAIF, a feedback-enhanced generalized alpha-investing framework that dynamically adjusts thresholds using revealed outcomes.
• Score: 18.22414171961847
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study online multiple testing with feedback, where decisions are made sequentially and the true state of the hypothesis is revealed after the decision has been made, either instantly or with a delay. We propose GAIF, a feedback-enhanced generalized alpha-investing framework that dynamically adjusts thresholds using revealed outcomes, ensuring finite-sample false discovery rate (FDR)/marginal FDR control. Extending GAIF to online conformal testing, we construct independent conformal $p$-values and introduce a feedback-driven model selection criterion to identify the best model/score, thereby improving statistical power. We demonstrate the effectiveness of our methods through numerical simulations and real-data applications.

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