English

Proper Calibeating

Theoretical Economics 2026-05-28 v1 Computer Science and Game Theory Machine Learning Machine Learning

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 proper\textit{proper} scoring rules (for which the best forecast is the true distribution) and define proper-calibration\textit{proper-calibration} and proper-calibeating\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.

Cite

@article{arxiv.2605.26703,
  title  = {Proper Calibeating},
  author = {Dean P. Foster and Sergiu Hart},
  journal= {arXiv preprint arXiv:2605.26703},
  year   = {2026}
}