Anytime-Valid Conformal Risk Control
This work addresses the need for robust uncertainty quantification in predictive tasks, particularly under distribution shift, but is incremental as it builds on existing conformal prediction methods.
The paper tackles the problem of ensuring statistically valid error control for prediction sets at any time point with a growing calibration dataset, extending beyond average control over fixed datasets, and demonstrates tight guarantees through simulations and real-world examples.
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.