# Achieving Risk Control in Online Learning Settings

arXiv: https://arxiv.org/abs/2205.09095 · HTML: https://mlsanity.com/paper/2205.09095/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 50 references that are in the map.
- First posted on arXiv 18 May 2022.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (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)
- [Sparsity Invariant CNNs](https://mlsanity.com/paper/1708.06500/) (2017)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [SMAC3: A Versatile Bayesian Optimization Package for Hyperparameter Optimization](https://mlsanity.com/paper/2109.09831/) (2021)
- [Learning to Recover 3D Scene Shape from a Single Image](https://mlsanity.com/paper/2012.09365/) (2020)
- [BinsFormer: Revisiting Adaptive Bins for Monocular Depth Estimation](https://mlsanity.com/paper/2204.00987/) (2022)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [DepthFormer: Exploiting Long-Range Correlation and Local Information for Accurate Monocular Depth Estimation](https://mlsanity.com/paper/2203.14211/) (2022)
- [Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imaging](https://mlsanity.com/paper/2202.05265/) (2022)
- [Distributional conformal prediction](https://mlsanity.com/paper/1909.07889/) (2019)
- [Robust Validation: Confident Predictions Even When Distributions Shift](https://mlsanity.com/paper/2008.04267/) (2020)
- [Beyond Pinball Loss: Quantile Methods for Calibrated Uncertainty Quantification](https://mlsanity.com/paper/2011.09588/) (2020)
- [Conformal Prediction using Conditional Histograms](https://mlsanity.com/paper/2105.08747/) (2021)
- [Don't Forget The Past: Recurrent Depth Estimation from Monocular Video](https://mlsanity.com/paper/2001.02613/) (2020)
- [Exact and Robust Conformal Inference Methods for Predictive Machine Learning With Dependent Data](https://mlsanity.com/paper/1802.06300/) (2018)
- [Flexible distribution-free conditional predictive bands using density estimators](https://mlsanity.com/paper/1910.05575/) (2019)
- [Improving Conditional Coverage via Orthogonal Quantile Regression](https://mlsanity.com/paper/2106.00394/) (2021)

## Built on by (most cited first, 30 of 39)

- [Conformal PID Control for Time Series Prediction](https://mlsanity.com/paper/2307.16895/) (2023)
- [Online conformal prediction with decaying step sizes](https://mlsanity.com/paper/2402.01139/) (2024)
- [Conformal Decision Theory: Safe Autonomous Decisions from Imperfect Predictions](https://mlsanity.com/paper/2310.05921/) (2023)
- [Fast yet Safe: Early-Exiting with Risk Control](https://mlsanity.com/paper/2405.20915/) (2024)
- [Non-Exchangeable Conformal Risk Control](https://mlsanity.com/paper/2310.01262/) (2023)
- [Conformal Validity Guarantees Exist for Any Data Distribution (and How to Find Them)](https://mlsanity.com/paper/2405.06627/) (2024)
- [Localized Adaptive Risk Control](https://mlsanity.com/paper/2405.07976/) (2024)
- [Kernel-based Optimally Weighted Conformal Time-Series Prediction](https://mlsanity.com/paper/2405.16828/) (2024)
- [Bellman Conformal Inference: Calibrating Prediction Intervals For Time Series](https://mlsanity.com/paper/2402.05203/) (2024)
- [The Relationship between No-Regret Learning and Online Conformal Prediction](https://mlsanity.com/paper/2502.10947/) (2025)
- [Early Time Classification with Accumulated Accuracy Gap Control](https://mlsanity.com/paper/2402.00857/) (2024)
- [Bayesian Optimization with Formal Safety Guarantees via Online Conformal Prediction](https://mlsanity.com/paper/2306.17815/) (2023)
- [On Continuous Monitoring of Risk Violations under Unknown Shift](https://mlsanity.com/paper/2506.16416/) (2025)
- [Conformal Prediction and Human Decision Making](https://mlsanity.com/paper/2503.11709/) (2025)
- [Cross-Validation Conformal Risk Control](https://mlsanity.com/paper/2401.11974/) (2024)
- [Mirror Online Conformal Prediction with Intermittent Feedback](https://mlsanity.com/paper/2503.10345/) (2025)
- [Conformal Information Pursuit for Interactively Guiding Large Language Models](https://mlsanity.com/paper/2507.03279/) (2025)
- [Guaranteed Dynamic Scheduling of Ultra-Reliable Low-Latency Traffic via Conformal Prediction](https://mlsanity.com/paper/2302.07675/) (2023)
- [Conformal Distributed Remote Inference in Sensor Networks Under Reliability and Communication Constraints](https://mlsanity.com/paper/2409.07902/) (2024)
- [Conformal Policy Control](https://mlsanity.com/paper/2603.02196/) (2026)
- [CHAMP: Conformalized 3D Human Multi-Hypothesis Pose Estimators](https://mlsanity.com/paper/2407.06141/) (2024)
- [Exploring the Noise Robustness of Online Conformal Prediction](https://mlsanity.com/paper/2501.18363/) (2025)
- [Valid Selection among Conformal Sets](https://mlsanity.com/paper/2506.20173/) (2025)
- [Online Conformal Prediction with Efficiency Guarantees](https://mlsanity.com/paper/2507.02496/) (2025)
- [Dynamic Estimation Loss Control in Variational Quantum Sensing via Online Conformal Inference](https://mlsanity.com/paper/2505.23389/) (2025)
- [Conformal Prediction with Corrupted Labels: Uncertain Imputation and Robust Re-weighting](https://mlsanity.com/paper/2505.04733/) (2025)
- [Multi-model Online Conformal Prediction with Graph-Structured Feedback](https://mlsanity.com/paper/2506.20898/) (2025)
- [Prediction-Powered Communication with Distortion Guarantees](https://mlsanity.com/paper/2509.24373/) (2025)
- [Conformal Risk Control under Non-Monotone Losses: Theory and Finite-Sample Guarantees](https://mlsanity.com/paper/2604.01502/) (2026)
- [Calibrated Multi-Level Quantile Forecasting](https://mlsanity.com/paper/2512.23671/) (2025)

## Abstract (arXiv)

To provide rigorous uncertainty quantification for online learning models, we develop a framework for constructing uncertainty sets that provably control risk -- such as coverage of confidence intervals, false negative rate, or F1 score -- in the online setting. This extends conformal prediction to apply to a larger class of online learning problems. Our method guarantees risk control at any user-specified level even when the underlying data distribution shifts drastically, even adversarially, over time in an unknown fashion. The technique we propose is highly flexible as it can be applied with any base online learning algorithm (e.g., a deep neural network trained online), requiring minimal implementation effort and essentially zero additional computational cost. We further extend our approach to control multiple risks simultaneously, so the prediction sets we generate are valid for all given risks. To demonstrate the utility of our method, we conduct experiments on real-world tabular time-series data sets showing that the proposed method rigorously controls various natural risks. Furthermore, we show how to construct valid intervals for an online image-depth estimation problem that previous sequential calibration schemes cannot handle.