# Delayed Feedback with Finite Tracking Capacity

Online conformal risk control has assumed each round's loss arrives immediately and intact, yet real systems delay feedback and can track only a limited number of pending predictions, so some feedback is lost for good. CA-OCRC designs the tracking policy and the prediction sets together: each round draws a random proxy delay, is tracked while capacity allows until its feedback arrives or the proxy delay expires, and a two-level inverse probability weighting compensates for lost feedback. Risk bounds for arbitrary and stochastic delays follow, and optimizing the proxy delay distribution shows that capacity growing only logarithmically in the maximum delay suffices to match the convergence rate of OCRC with unlimited feedback.

Online conformal risk control has assumed each round's loss arrives immediately and intact, yet real systems delay feedback and can track only a limited number of pending predictions, so some feedback is lost for good. CA-OCRC designs the tracking policy and the prediction sets together: each round draws a random proxy delay, is tracked while capacity allows until its feedback arrives or the proxy delay expires, and a two-level inverse probability weighting compensates for lost feedback. Risk bounds for arbitrary and stochastic delays follow, and optimizing the proxy delay distribution shows that capacity growing only logarithmically in the maximum delay suffices to match the convergence rate of OCRC with unlimited feedback.