# On Continuous Monitoring of Risk Violations under Unknown Shift

arXiv: https://arxiv.org/abs/2506.16416 · HTML: https://mlsanity.com/paper/2506.16416/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 60 references that are in the map.
- First posted on arXiv 19 Jun 2025.

## Builds on (most cited first, 30 of 48)

- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [A Comprehensive Survey on Test-Time Adaptation under Distribution Shifts](https://mlsanity.com/paper/2303.15361/) (2023)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Functional Map of the World](https://mlsanity.com/paper/1711.07846/) (2017)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [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)
- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [Estimating means of bounded random variables by betting](https://mlsanity.com/paper/2010.09686/) (2020)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Game-theoretic statistics and safe anytime-valid inference](https://mlsanity.com/paper/2210.01948/) (2022)
- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [Localized Conformal Prediction: A Generalized Inference Framework for Conformal Prediction](https://mlsanity.com/paper/2106.08460/) (2021)
- [Is Out-of-Distribution Detection Learnable?](https://mlsanity.com/paper/2210.14707/) (2022)
- [Safe Testing](https://mlsanity.com/paper/1906.07801/) (2019)
- [Distribution-free uncertainty quantification for classification under label shift](https://mlsanity.com/paper/2103.03323/) (2021)
- [Agreement-on-the-Line: Predicting the Performance of Neural Networks under Distribution Shift](https://mlsanity.com/paper/2206.13089/) (2022)
- [Wild-Time: A Benchmark of in-the-Wild Distribution Shift over Time](https://mlsanity.com/paper/2211.14238/) (2022)
- [Distribution-free binary classification: prediction sets, confidence intervals and calibration](https://mlsanity.com/paper/2006.10564/) (2020)
- [Hypothesis testing with e-values](https://mlsanity.com/paper/2410.23614/) (2024)
- [Online conformal prediction with decaying step sizes](https://mlsanity.com/paper/2402.01139/) (2024)
- [Tracking the risk of a deployed model and detecting harmful distribution shifts](https://mlsanity.com/paper/2110.06177/) (2021)
- [Achieving Risk Control in Online Learning Settings](https://mlsanity.com/paper/2205.09095/) (2022)
- [Nonparametric Two-Sample Testing by Betting](https://mlsanity.com/paper/2112.09162/) (2021)
- [Testing randomness](https://mlsanity.com/paper/1906.09256/) (2019)
- [Retrain or not retrain: Conformal test martingales for change-point detection](https://mlsanity.com/paper/2102.10439/) (2021)
- [E-detectors: a nonparametric framework for sequential change detection](https://mlsanity.com/paper/2203.03532/) (2022)

## Built on by (most cited first, 10 of 10)

- [E-valuator: Reliable Agent Verifiers with Sequential Hypothesis Testing](https://mlsanity.com/paper/2512.03109/) (2025)
- [Monitoring Risks in Test-Time Adaptation](https://mlsanity.com/paper/2507.08721/) (2025)
- [Testing For Distribution Shifts with Conditional Conformal Test Martingales](https://mlsanity.com/paper/2602.13848/) (2026)
- [Prediction-Powered Risk Monitoring of Deployed Models for Detecting Harmful Distribution Shifts](https://mlsanity.com/paper/2602.02229/) (2026)
- [Certified Adaptive Refresh: Anytime-Valid Monitoring for Federated Conformal RAG](https://mlsanity.com/paper/2605.29139/) (2026)
- [Detecting Object Tracking Failure via Sequential Hypothesis Testing](https://mlsanity.com/paper/2602.12983/) (2026)
- [Incentive Aware AI Regulations: A Credal Characterisation](https://mlsanity.com/paper/2603.05175/) (2026)
- [Online Safety Monitoring for LLMs](https://mlsanity.com/paper/2607.02510/) (2026)
- [When Can Old Evaluations Certify a New Model? Label-Efficient Release Decisions under Evaluator Drift](https://mlsanity.com/paper/2609.32267/) (2026)
- [Runtime Monitoring of Supermartingale Certificates](https://mlsanity.com/paper/2610.19701/) (2026)

## Abstract (arXiv)

Machine learning systems deployed in the real world must operate under dynamic and often unpredictable distribution shifts. This challenges the validity of statistical safety assurances on the system's risk established beforehand. Common risk control frameworks rely on fixed assumptions and lack mechanisms to continuously monitor deployment reliability. In this work, we propose a general framework for the real-time monitoring of risk violations in evolving data streams. Leveraging the 'testing by betting' paradigm, we propose a sequential hypothesis testing procedure to detect violations of bounded risks associated with the model's decision-making mechanism, while ensuring control on the false alarm rate. Our method operates under minimal assumptions on the nature of encountered shifts, rendering it broadly applicable. We illustrate the effectiveness of our approach by monitoring risks in outlier detection and set prediction under a variety of shifts.