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.

Conformal prediction is an emerging technique for uncertainty quantification that constructs prediction sets guaranteed to contain the true label with a predefined probability. Recent work develops online conformal prediction methods that adaptively construct prediction sets to accommodate distribution shifts. However, existing algorithms typically assume *perfect label accuracy* which rarely holds in practice. In this work, we investigate the robustness of online conformal prediction under uniform label noise with a known noise rate. We show that label noise causes a persistent gap between the actual mis-coverage rate and the desired rate $\alpha$, leading to either overestimated or underestimated coverage guarantees. To address this issue, we propose a novel loss function *robust pinball loss*, which provides an unbiased estimate of clean pinball loss without requiring ground-truth labels. Theoretically, we demonstrate that robust pinball loss enables online conformal prediction to eliminate the coverage gap under uniform label noise, achieving a convergence rate of $\mathcal{O}(T^{-1/2})$ for both empirical and expected coverage errors (i.e., absolute deviation of the empirical and expected mis-coverage rate from the target level $\alpha$). This loss offers a general solution to the uniform label noise, and is complementary to existing online conformal prediction methods. Extensive experiments demonstrate that the proposed loss enhances the noise robustness of various online conformal prediction methods by achieving a precise coverage guarantee.

Conformal prediction is a statistical framework that generates prediction sets containing ground-truth labels with a desired coverage guarantee. The predicted probabilities produced by machine learning models are generally miscalibrated, leading to large prediction sets in conformal prediction. To address this issue, we propose a novel algorithm named $\textit{Sorted Adaptive Prediction Sets}$ (SAPS), which discards all the probability values except for the maximum softmax probability. The key idea behind SAPS is to minimize the dependence of the non-conformity score on the probability values while retaining the uncertainty information. In this manner, SAPS can produce compact prediction sets and communicate instance-wise uncertainty. Extensive experiments validate that SAPS not only lessens the prediction sets but also broadly enhances the conditional coverage rate of prediction sets.