Instance-Adaptive Online Multicalibration

2026-05-09

AI Summary

This work addresses the challenge of online multicalibration under shifting data distributions, where existing methods struggle to simultaneously guarantee strong performance in both worst-case and benign scenarios. The authors propose an adaptive algorithm that dynamically refines a dyadic grid over predicted values and interpolates across varying data environments, achieving the first automatic adaptation to multiple distributional assumptions—such as marginal randomness, J-segment piecewise stationarity, and adversarial settings. By integrating online learning with multicalibration theory, the method introduces an instance-dependent analysis framework based on threshold complexity. It attains near-optimal regret bounds: Õ(T^{2/3}) in the worst case, Õ(√T) under marginal randomness, and Õ(√{JT}) for J-segment piecewise stationary means, with all bounds shown to be tight up to logarithmic factors.

Abstract

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 $\widetilde O(T^{2/3})$ worst-case-optimal rate for online multicalibration, while simultaneously automatically adapting to easier instances: in the marginal stochastic setting it obtains a rate of $\widetilde O(\sqrt T)$, and for piecewise-stationary means with $J$ segments its rate is $\widetilde O(\sqrt{JT})$. 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.

Problem

• online multicalibration
• instance-adaptive
• dyadic grid
• threshold-complexity
• prediction calibration

Innovation

• online multicalibration
• instance-adaptive
• dyadic grid refinement
• threshold complexity
• piecewise-stationary