# Proper Calibeating

arXiv: https://arxiv.org/abs/2605.26703 · HTML: https://mlsanity.com/paper/2605.26703/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 30 references that are in the map.
- First posted on arXiv 26 May 2026.

## Builds on (most cited first, 14 of 14)

- [U-Calibration: Forecasting for an Unknown Agent](https://mlsanity.com/paper/2307.00168/) (2023)
- [Stronger Calibration Lower Bounds via Sidestepping](https://mlsanity.com/paper/2012.03454/) (2020)
- [When Does Optimizing a Proper Loss Yield Calibration?](https://mlsanity.com/paper/2305.18764/) (2023)
- [Online Minimax Multiobjective Optimization: Multicalibeating and Other Applications](https://mlsanity.com/paper/2108.03837/) (2021)
- [Evaluating probabilistic classifiers: Reliability diagrams and score decompositions revisited](https://mlsanity.com/paper/2008.03033/) (2020)
- [Smooth Calibration, Leaky Forecasts, Finite Recall, and Nash Dynamics](https://mlsanity.com/paper/2210.07152/) (2022)
- [Forecast Hedging and Calibration](https://mlsanity.com/paper/2210.07169/) (2022)
- [Calibrated Forecasts: The Minimax Proof](https://mlsanity.com/paper/2209.05863/) (2022)
- ["Calibeating": Beating Forecasters at Their Own Game](https://mlsanity.com/paper/2209.04892/) (2022)
- [Faster Recalibration of an Online Predictor via Approachability](https://mlsanity.com/paper/2310.17002/) (2023)
- [Consistent and Asymptotically Unbiased Estimation of Proper Calibration Errors](https://mlsanity.com/paper/2312.08589/) (2023)
- [Simultaneous Swap Regret Minimization via KL-Calibration](https://mlsanity.com/paper/2502.16387/) (2025)
- [Calibeating Made Simple](https://mlsanity.com/paper/2603.22167/) (2026)
- [Calibrated Probabilistic Forecasts for Arbitrary Sequences](https://mlsanity.com/paper/2409.19157/) (2024)

## Built on by (most cited first, 1 of 1)

- [Optimal Recalibration of an Online Predictor](https://mlsanity.com/paper/2607.19689/) (2026)

## Abstract (arXiv)

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 scoring rules (for which the true distribution is an optimal forecast) and define textitproper calibration and textitproper calibeating by requiring the corresponding guarantees to hold 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; in particular, textitcomplete calibeating---a strong form of calibeating that calibeats the joint binning---is always proper. Finally, we consider textitdecision-making under uncertainty, where one best replies to the forecasts. We establish that (proper) calibration is equivalent to universal no regret, and (proper) complete calibeating is equivalent to universal no regret together with universal subsuming of the reference sequence, where textituniversal refers to all bounded utility functions.