  We develop methods for forming prediction sets in an online setting where the
data generating distribution is allowed to vary over time in an unknown
fashion. Our framework builds on ideas from conformal inference to provide a
general wrapper that can be combined with any black box method that produces
point predictions of the unseen label or estimated quantiles of its
distribution. While previous conformal inference methods rely on the assumption
that the data points are exchangeable, our adaptive approach provably achieves
the desired coverage frequency over long-time intervals irrespective of the
true data generating process. We accomplish this by modelling the distribution
shift as a learning problem in a single parameter whose optimal value is
varying over time and must be continuously re-estimated. We test our method,
adaptive conformal inference, on two real world datasets and find that its
predictions are robust to visible and significant distribution shifts.
