Résumé
Uncertainty quantification has received considerable interestin recent works in Machine Learning. In particular, Conformal Prediction(CP) gains ground in this field. For the case of time series, OnlineConformal Prediction (OCP) becomes an option to address the problemof data distribution shift over time. Indeed, the idea of OCP is to updatea threshold of some quantity (whether the miscoverage level or the quantile)based on the distribution observation. To evaluate the performanceof OCP methods, two key aspects are typically considered: the coveragevalidity and the prediction interval width minimization. Recently,new OCP methods have emerged, offering long-run coverage guaranteesand producing more informative intervals. However, during the thresholdupdate step, most of these methods focus solely on the validity ofthe prediction intervals – that is, whether the ground truth falls insideor outside the interval – without accounting for their relevance. In thispaper, we aim to leverage this overlooked aspect. Specifically, we proposeenhancing the threshold update step by replacing the binary evaluation(inside/outside) with a broader class of functions that quantify the relevanceof the prediction interval using the ground truth. This approachhelps prevent abrupt threshold changes, potentially resulting in narrowerprediction intervals. Indeed, experimental results on real-world datasetssuggest that these functions can produce tighter intervals compared toexisting OCP methods while maintaining coverage validity.