Proper Calibeating

Abstract:The classic concept of "calibrated forecasts" and its more recent refinement, "calibeating," are defined with respect to the standard quadratic scoring rule. We extend these notions to the class of $\textit{proper}$ scoring rules (for which the best forecast is the true distribution) and define $\textit{proper-calibration}$ and $\textit{proper-calibeating}$ by requiring the errors to converge to zero uniformly over all bounded proper scoring rules. We first establish that calibration always implies proper-calibration, whereas calibeating need not imply proper-calibeating. Second, we show how to guarantee proper-calibeating and proper-multicalibeating. Finally, we demonstrate the equivalence between proper-calibration and universal no regret when best replying to forecasts in decision-making under uncertainty.

Theoretical Economics (econ.TH); Computer Science and Game Theory (cs.GT); Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2605.26703 [econ.TH]

(or arXiv:2605.26703v2 [econ.TH] for this version)

https://doi.org/10.48550/arXiv.2605.26703 Focus to learn more arXiv-issued DOI via DataCite

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