# Exploring the Noise Robustness of Online Conformal Prediction

arXiv: https://arxiv.org/abs/2501.18363 · HTML: https://mlsanity.com/paper/2501.18363/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 68 references that are in the map.
- First posted on arXiv 30 Jan 2025.

## Builds on (most cited first, 30 of 46)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Online Learning: A Modern Introduction Using Convex Optimization](https://mlsanity.com/paper/1912.13213/) (2019)
- [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)
- [Combating noisy labels by agreement: A joint training method with co-regularization](https://mlsanity.com/paper/2003.02752/) (2020)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [Are Anchor Points Really Indispensable in Label-Noise Learning?](https://mlsanity.com/paper/1906.00189/) (2019)
- [Online Learning: A Comprehensive Survey](https://mlsanity.com/paper/1802.02871/) (2018)
- [Handbook of Convergence Theorems for (Stochastic) Gradient Methods](https://mlsanity.com/paper/2301.11235/) (2023)
- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Provably End-to-end Label-Noise Learning without Anchor Points](https://mlsanity.com/paper/2102.02400/) (2021)
- [Large language model validity via enhanced conformal prediction methods](https://mlsanity.com/paper/2406.09714/) (2024)
- [Scale-Free Online Learning](https://mlsanity.com/paper/1601.01974/) (2016)
- [Beyond Class-Conditional Assumption: A Primary Attempt to Combat Instance-Dependent Label Noise](https://mlsanity.com/paper/2012.05458/) (2020)
- [Uncertainty Quantification over Graph with Conformalized Graph Neural Networks](https://mlsanity.com/paper/2305.14535/) (2023)
- [Improved Online Conformal Prediction via Strongly Adaptive Online Learning](https://mlsanity.com/paper/2302.07869/) (2023)
- [Open-set Label Noise Can Improve Robustness Against Inherent Label Noise](https://mlsanity.com/paper/2106.10891/) (2021)
- [Online conformal prediction with decaying step sizes](https://mlsanity.com/paper/2402.01139/) (2024)
- [Conformal Alignment: Knowing When to Trust Foundation Models with Guarantees](https://mlsanity.com/paper/2405.10301/) (2024)
- [Conformal Prediction for Deep Classifier via Label Ranking](https://mlsanity.com/paper/2310.06430/) (2023)
- [Improved Strongly Adaptive Online Learning using Coin Betting](https://mlsanity.com/paper/1610.04578/) (2016)
- [Prediction and outlier detection in classification problems](https://mlsanity.com/paper/1905.04396/) (2019)

## Built on by (most cited first, 5 of 5)

- [Mirror Online Conformal Prediction with Intermittent Feedback](https://mlsanity.com/paper/2503.10345/) (2025)
- [When Does Trimming Help Conformal Prediction? A Retained-Law Diagnostic under Calibration Contamination](https://mlsanity.com/paper/2605.06204/) (2026)
- [Delving into Non-Exchangeability for Conformal Prediction in Graph-Structured Multivariate Time Series](https://mlsanity.com/paper/2605.04957/) (2026)
- [Online Conformal Prediction with Corrupted Feedback](https://mlsanity.com/paper/2605.20515/) (2026)
- [CHOIR: heterogeneity-aware conformal prediction for crash injury severity across driver safety strata](https://mlsanity.com/paper/2609.11592/) (2026)

## Abstract (arXiv)

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, in both constant and dynamic learning rate schedules. We show that label noise causes a persistent gap between the actual mis-coverage rate and the desired rate α, leading to either overestimated or underestimated coverage guarantees. To address this issue, we propose Noise Robust Online Conformal Prediction (dubbed NR-OCP) by updating the threshold with a novel robust pinball loss, which provides an unbiased estimate of clean pinball loss without requiring ground-truth labels. Our theoretical analysis shows that NR-OCP eliminates the coverage gap in both constant and dynamic learning rate schedules, achieving a convergence rate of O(T-1/2) for both empirical and expected coverage errors under uniform label noise. Extensive experiments demonstrate the effectiveness of our method by achieving both precise coverage and improved efficiency.