An Elementary Predictor Obtaining $2\sqrt{T}$ Distance to Calibration
Eshwar Ram Arunachaleswaran Natalie Collina Aaron Roth Mirah Shi
Blasiok et al. [2023] proposed distance to calibration as a natural measure
of calibration error that unlike expected calibration error (ECE) is
continuous. Recently, Qiao and Zheng [2024] gave a non-constructive argument
establishing the existence of an online predictor that can obtain $O(\sqrt{T})$
distance to calibration in the adversarial setting, which is known to be
impossible for ECE. They leave as an open problem finding an explicit,
efficient algorithm. We resolve this problem and give an extremely simple,
efficient, deterministic algorithm that obtains distance to calibration error
at most $2\sqrt{T}$.