2026/05/10 by Zhiming Huang, Jamie Morgenstern, Aaron Roth +1 · 1 voice
#cs.LG
We study online multicalibration beyond the worst-case. We give a single, efficient algorithm which dynamically interpolates between benign and worst-case sequences by adaptively refining a dyadic grid of prediction values. Its error is controlled by the number of leaves in the refinement tree. Our analysis recovers the known \widetilde O(T2/3) worst-case-optimal rate for online multicalibration, while simultaneously automatically adapting to easier instances: in the marginal stochastic setting it obtains a rate of \widetilde O(√ T), and for piecewise-stationary means with J segments its rate is \widetilde O(√(JT)). More generally, the rate depends on a threshold-complexity measure of the predictable mean process relative to the group family. We show that this dependence is tight up to logarithmic factors.