# Calibrated Forecasts: The Minimax Proof

arXiv: https://arxiv.org/abs/2209.05863 · HTML: https://mlsanity.com/paper/2209.05863/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 9 references that are in the map.
- First posted on arXiv 13 Sep 2022.

## Builds on (most cited first, 2 of 2)

- [Stronger Calibration Lower Bounds via Sidestepping](https://mlsanity.com/paper/2012.03454/) (2020)
- ["Calibeating": Beating Forecasters at Their Own Game](https://mlsanity.com/paper/2209.04892/) (2022)

## Built on by (most cited first, 17 of 17)

- [U-Calibration: Forecasting for an Unknown Agent](https://mlsanity.com/paper/2307.00168/) (2023)
- [A Unifying Perspective on Multi-Calibration: Game Dynamics for Multi-Objective Learning](https://mlsanity.com/paper/2302.10863/) (2023)
- [Calibrated Stackelberg Games: Learning Optimal Commitments Against Calibrated Agents](https://mlsanity.com/paper/2306.02704/) (2023)
- [Forecast Hedging and Calibration](https://mlsanity.com/paper/2210.07169/) (2022)
- [Classifier Calibration with ROC-Regularized Isotonic Regression](https://mlsanity.com/paper/2311.12436/) (2023)
- [On the Distance from Calibration in Sequential Prediction](https://mlsanity.com/paper/2402.07458/) (2024)
- [Calibration Error for Decision Making](https://mlsanity.com/paper/2404.13503/) (2024)
- [Optimal Multiclass U-Calibration Error and Beyond](https://mlsanity.com/paper/2405.19374/) (2024)
- [High dimensional online calibration in polynomial time](https://mlsanity.com/paper/2504.09096/) (2025)
- [High-Dimensional Calibration from Swap Regret](https://mlsanity.com/paper/2505.21460/) (2025)
- [Truthfulness of Calibration Measures](https://mlsanity.com/paper/2407.13979/) (2024)
- [Learning With Multi-Group Guarantees For Clusterable Subpopulations](https://mlsanity.com/paper/2410.14588/) (2024)
- [Computational and Statistical Hardness of Calibration Distance](https://mlsanity.com/paper/2603.18391/) (2026)
- [Instance-Adaptive Online Multicalibration](https://mlsanity.com/paper/2605.09273/) (2026)
- [Proper Calibeating](https://mlsanity.com/paper/2605.26703/) (2026)
- [Efficient Sequential Calibration with O(T2/3-ε) Error Bound](https://mlsanity.com/paper/2607.12928/) (2026)
- [Improved and Oracle-Efficient Online ℓ1-Multicalibration](https://mlsanity.com/paper/2505.17365/) (2025)

## Abstract (arXiv)

A formal write-up of the simple proof (1995) of the existence of calibrated forecasts by the minimax theorem, which moreover shows that N3 periods suffice to guarantee a calibration error of at most 1/N.