Online conformal prediction with decaying step sizes

We study the problem of online uncertainty quantification, such as that encountered in time-series forecasting. Our goal is to produce a prediction set at each time, based on all previous information, that contain the true label with a specified coverage probability. Such prediction sets are useful to the point of being requirements in many sequential problems, including medicine [Robinson, 1978], robotics [Lindemann et al., 2023], finance [Mykland, 2003], and epidemiology [Cramer et al., 2022]. Given this broad utility, it comes as no surprise that prediction sets have been studied for approximately one hundred years (and possibly more; see Section 1.1 of Tian et al. [2022]).