# Anytime-Valid Conformal Risk Control

arXiv: https://arxiv.org/abs/2602.04364 · HTML: https://mlsanity.com/paper/2602.04364/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 20 references that are in the map.
- First posted on arXiv 4 Feb 2026.

## Builds on (most cited first, 12 of 12)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [Time-uniform, nonparametric, nonasymptotic confidence sequences](https://mlsanity.com/paper/1810.08240/) (2018)
- [Estimating means of bounded random variables by betting](https://mlsanity.com/paper/2010.09686/) (2020)
- [Anytime-valid off-policy inference for contextual bandits](https://mlsanity.com/paper/2210.10768/) (2022)
- [Sequential estimation of quantiles with applications to A/B-testing and best-arm identification](https://mlsanity.com/paper/1906.09712/) (2019)
- [Universal distribution of the empirical coverage in split conformal prediction](https://mlsanity.com/paper/2303.02770/) (2023)
- [Active, anytime-valid risk controlling prediction sets](https://mlsanity.com/paper/2406.10490/) (2024)
- [Training-Conditional Coverage Bounds under Covariate Shift](https://mlsanity.com/paper/2405.16594/) (2024)
- [Distribution-Free Finite-Sample Guarantees and Split Conformal Prediction](https://mlsanity.com/paper/2210.14735/) (2022)
- [Probabilistic Conformal Coverage Guarantees in Small-Data Settings](https://mlsanity.com/paper/2509.15349/) (2025)

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

- [ToolChain-CRC: Conformal Risk Control for Agentic AI Under Retrieval and Tool-Use Drift](https://mlsanity.com/paper/2606.18467/) (2026)
- [A Joint Finite-Sample Certificate for Adaptive Selective Conformal Risk Control](https://mlsanity.com/paper/2606.08517/) (2026)
- [When Can Conformal Risk Control Certify LLM Outputs? Bounds, Impossibility, and Adaptation for Structured Generation](https://mlsanity.com/paper/2606.29054/) (2026)
- [Certified Adaptive Refresh: Anytime-Valid Monitoring for Federated Conformal RAG](https://mlsanity.com/paper/2605.29139/) (2026)
- [Sequential Confidence Sets for Coverage-Constrained Conformal Model Selection](https://mlsanity.com/paper/2609.28522/) (2026)

## Abstract (arXiv)

Prediction sets provide a means of quantifying the uncertainty in predictive tasks. Using held out calibration data, conformal prediction and risk control can produce prediction sets that exhibit statistically valid error control in a computationally efficient manner. However, in the standard formulations, the error is only controlled on average over many possible calibration datasets of fixed size. In this paper, we extend the control to remain valid with high probability over a cumulatively growing calibration dataset at any time point. We derive such guarantees using quantile-based arguments and illustrate the applicability of the proposed framework to settings involving distribution shift. We further establish a matching lower bound and show that our guarantees are asymptotically tight. Finally, we demonstrate the practical performance of our methods through both simulations and real-world numerical examples.