# Online Conformal Selection with Accept-to-Reject Changes

arXiv: https://arxiv.org/abs/2508.13838 · HTML: https://mlsanity.com/paper/2508.13838/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 35 references that are in the map.
- First posted on arXiv 19 Aug 2025.

## Builds on (most cited first, 18 of 18)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [CoQA: A Conversational Question Answering Challenge](https://mlsanity.com/paper/1808.07042/) (2018)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [Improved Online Conformal Prediction via Strongly Adaptive Online Learning](https://mlsanity.com/paper/2302.07869/) (2023)
- [Selection by Prediction with Conformal p-values](https://mlsanity.com/paper/2210.01408/) (2022)
- [Conformal Prediction for Deep Classifier via Label Ranking](https://mlsanity.com/paper/2310.06430/) (2023)
- [Model-free selective inference under covariate shift via weighted conformal p-values](https://mlsanity.com/paper/2307.09291/) (2023)
- [Online Rules for Control of False Discovery Rate and False Discovery Exceedance](https://mlsanity.com/paper/1603.09000/) (2016)
- [Confidence on the Focal: Conformal Prediction with Selection-Conditional Coverage](https://mlsanity.com/paper/2403.03868/) (2024)
- [Online multiple testing with e-values](https://mlsanity.com/paper/2311.06412/) (2023)
- [Does confidence calibration improve conformal prediction?](https://mlsanity.com/paper/2402.04344/) (2024)
- [Selective conformal inference with false coverage-statement rate control](https://mlsanity.com/paper/2301.00584/) (2023)
- [CAP: A General Algorithm for Online Selective Conformal Prediction with FCR Control](https://mlsanity.com/paper/2403.07728/) (2024)
- [Parametric Scaling Law of Tuning Bias in Conformal Prediction](https://mlsanity.com/paper/2502.03023/) (2025)

## Built on by (most cited first, 3 of 3)

- [Conformal Selective Prediction with General Risk Control](https://mlsanity.com/paper/2603.24704/) (2026)
- [Model-agnostic Selective Labeling with Provable Statistical Guarantees](https://mlsanity.com/paper/2510.14581/) (2025)
- [Beyond Fixed False Discovery Rates: Post-Hoc Conformal Selection with E-Variables](https://mlsanity.com/paper/2604.11305/) (2026)

## Abstract (arXiv)

Selecting a subset of promising candidates from a large pool is crucial across various scientific and real-world applications. Conformal selection offers a distribution-free and model-agnostic framework for candidate selection with uncertainty quantification. While effective in offline settings, its application to online scenarios, where data arrives sequentially, poses challenges. Notably, conformal selection permits the deselection of previously selected candidates, which is incompatible with applications requiring irreversible selection decisions. This limitation is particularly evident in resource-intensive sequential processes, such as drug discovery, where advancing a compound to subsequent stages renders reversal impractical. To address this issue, we extend conformal selection to an online Accept-to-Reject Changes (ARC) procedure: non-selected data points can be reconsidered for selection later, and once a candidate is selected, the decision is irreversible. Specifically, we propose a novel conformal selection method, Online Conformal Selection with Accept-to-Reject Changes (dubbed OCS-ARC), which incorporates online Benjamini-Hochberg procedure into the candidate selection process. We provide theoretical guarantees that OCS-ARC controls the false discovery rate (FDR) at or below the nominal level at any timestep under both i.i.d. and exchangeable data assumptions. Additionally, we theoretically show that our approach naturally extends to multivariate response settings. Extensive experiments on synthetic and real-world datasets demonstrate that OCS-ARC significantly improves selection power over the baseline while maintaining valid FDR control across all examined timesteps.