[2402.11410] An Elementary Predictor Obtaining $2\sqrt{T}+1$ Distance to Calibration
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Computer Science > Machine Learning

arXiv:2402.11410 (cs)
[Submitted on 18 Feb 2024 (v1), last revised 7 Oct 2024 (this version, v2)]

Title:An Elementary Predictor Obtaining $2\sqrt{T}+1$ Distance to Calibration

Authors:Eshwar Ram Arunachaleswaran, Natalie Collina, Aaron Roth, Mirah Shi
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Abstract: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 $2\sqrt{T}+1$.
Subjects: Machine Learning (cs.LG); Data Structures and Algorithms (cs.DS); Machine Learning (stat.ML)
Cite as: arXiv:2402.11410 [cs.LG]
  (or arXiv:2402.11410v2 [cs.LG] for this version)
  https://doi.org/10.48550/arXiv.2402.11410

Submission history

From: Mirah Shi [view email]
[v1] Sun, 18 Feb 2024 00:53:05 UTC (295 KB)
[v2] Mon, 7 Oct 2024 14:26:56 UTC (9 KB)
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