Calibeating Made Simple

Yurong Chen, Zhiyi Huang, Michael I. Jordan, Haipeng Luo
Proceedings of Thirty Ninth Conference on Learning Theory, PMLR 336:1373-1398, 2026.

Abstract

We study calibeating, the problem of post-processing external forecasts online to minimize cumulative losses and match an informativeness-based benchmark. Unlike prior work, which analyzed calibeating for specific losses with specific arguments, we reduce calibeating to existing online learning techniques and obtain results for general proper losses. More concretely, we first show that calibeating is minimax-equivalent to regret minimization. This recovers the $O(\log T)$ calibeating rate of Foster and Hart (2023) for the Brier and log losses and its optimality, and yields new optimal calibeating rates for exp-concave losses and general bounded losses. Second, we prove that multi-calibeating is minimax-equivalent to the combination of calibeating and the classical expert problem. This yields new optimal multi-calibeating rates for exp-concave losses, including Brier and log losses, and general bounded losses. Finally, we obtain new bounds for achieving calibeating and calibration simultaneously for the Brier loss. For binary predictions, our result gives the first calibrated algorithm that at the same time also achieves the optimal $O(\log T)$ calibeating rate.

Cite this Paper

BibTeX
@InProceedings{pmlr-v336-chen26h, title = {Calibeating Made Simple}, author = {Chen, Yurong and Huang, Zhiyi and Jordan, Michael I. and Luo, Haipeng}, booktitle = {Proceedings of Thirty Ninth Conference on Learning Theory}, pages = {1373--1398}, year = {2026}, editor = {Hanneke, Steve and Lattimore, Tor}, volume = {336}, series = {Proceedings of Machine Learning Research}, month = {29 Jun--03 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v336/main/assets/chen26h/chen26h.pdf}, url = {https://proceedings.mlr.press/v336/chen26h.html}, abstract = { We study calibeating, the problem of post-processing external forecasts online to minimize cumulative losses and match an informativeness-based benchmark. Unlike prior work, which analyzed calibeating for specific losses with specific arguments, we reduce calibeating to existing online learning techniques and obtain results for general proper losses. More concretely, we first show that calibeating is minimax-equivalent to regret minimization. This recovers the $O(\log T)$ calibeating rate of Foster and Hart (2023) for the Brier and log losses and its optimality, and yields new optimal calibeating rates for exp-concave losses and general bounded losses. Second, we prove that multi-calibeating is minimax-equivalent to the combination of calibeating and the classical expert problem. This yields new optimal multi-calibeating rates for exp-concave losses, including Brier and log losses, and general bounded losses. Finally, we obtain new bounds for achieving calibeating and calibration simultaneously for the Brier loss. For binary predictions, our result gives the first calibrated algorithm that at the same time also achieves the optimal $O(\log T)$ calibeating rate.} }
Endnote
%0 Conference Paper %T Calibeating Made Simple %A Yurong Chen %A Zhiyi Huang %A Michael I. Jordan %A Haipeng Luo %B Proceedings of Thirty Ninth Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2026 %E Steve Hanneke %E Tor Lattimore %F pmlr-v336-chen26h %I PMLR %P 1373--1398 %U https://proceedings.mlr.press/v336/chen26h.html %V 336 %X We study calibeating, the problem of post-processing external forecasts online to minimize cumulative losses and match an informativeness-based benchmark. Unlike prior work, which analyzed calibeating for specific losses with specific arguments, we reduce calibeating to existing online learning techniques and obtain results for general proper losses. More concretely, we first show that calibeating is minimax-equivalent to regret minimization. This recovers the $O(\log T)$ calibeating rate of Foster and Hart (2023) for the Brier and log losses and its optimality, and yields new optimal calibeating rates for exp-concave losses and general bounded losses. Second, we prove that multi-calibeating is minimax-equivalent to the combination of calibeating and the classical expert problem. This yields new optimal multi-calibeating rates for exp-concave losses, including Brier and log losses, and general bounded losses. Finally, we obtain new bounds for achieving calibeating and calibration simultaneously for the Brier loss. For binary predictions, our result gives the first calibrated algorithm that at the same time also achieves the optimal $O(\log T)$ calibeating rate.
APA
Chen, Y., Huang, Z., Jordan, M.I. & Luo, H.. (2026). Calibeating Made Simple. Proceedings of Thirty Ninth Conference on Learning Theory, in Proceedings of Machine Learning Research 336:1373-1398 Available from https://proceedings.mlr.press/v336/chen26h.html.

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