# Forecast Hedging and Calibration

arXiv: https://arxiv.org/abs/2210.07169 · HTML: https://mlsanity.com/paper/2210.07169/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 39 references that are in the map.
- First posted on arXiv 13 Oct 2022.

## Builds on (most cited first, 1 of 1)

- [Calibrated Forecasts: The Minimax Proof](https://mlsanity.com/paper/2209.05863/) (2022)

## Built on by (most cited first, 22 of 22)

- [Smooth ECE: Principled Reliability Diagrams via Kernel Smoothing](https://mlsanity.com/paper/2309.12236/) (2023)
- [A Unifying Theory of Distance from Calibration](https://mlsanity.com/paper/2211.16886/) (2022)
- [U-Calibration: Forecasting for an Unknown Agent](https://mlsanity.com/paper/2307.00168/) (2023)
- [Calibrated Stackelberg Games: Learning Optimal Commitments Against Calibrated Agents](https://mlsanity.com/paper/2306.02704/) (2023)
- [Classifier Calibration with ROC-Regularized Isotonic Regression](https://mlsanity.com/paper/2311.12436/) (2023)
- [The Relative Value of Prediction in Algorithmic Decision Making](https://mlsanity.com/paper/2312.08511/) (2023)
- [Calibration Error for Decision Making](https://mlsanity.com/paper/2404.13503/) (2024)
- [Simultaneous Swap Regret Minimization via KL-Calibration](https://mlsanity.com/paper/2502.16387/) (2025)
- [Online Platt Scaling with Calibeating](https://mlsanity.com/paper/2305.00070/) (2023)
- [In Defense of Defensive Forecasting](https://mlsanity.com/paper/2506.11848/) (2025)
- [Improved Bounds for Swap Multicalibration and Swap Omniprediction](https://mlsanity.com/paper/2505.20885/) (2025)
- [An Efficient Black-Box Reduction from Online Learning to Multicalibration, and a New Route to Phi-Regret Minimization](https://mlsanity.com/paper/2604.19592/) (2026)
- [Calibrated Multi-Level Quantile Forecasting](https://mlsanity.com/paper/2512.23671/) (2025)
- [Distribution free M-estimation](https://mlsanity.com/paper/2505.22807/) (2025)
- [Defensive Generation](https://mlsanity.com/paper/2602.21390/) (2026)
- [Brenier Isotonic Regression](https://mlsanity.com/paper/2603.10452/) (2026)
- [Proper Calibeating](https://mlsanity.com/paper/2605.26703/) (2026)
- [Blackwell Approachability and Gradient Equilibrium are Equivalent](https://mlsanity.com/paper/2606.27315/) (2026)
- [Regret, equilibrium, and learning in games: A guided tour](https://mlsanity.com/paper/2608.09389/) (2026)
- [Truthful Calibration Measures for Sequential Prediction](https://mlsanity.com/paper/2608.21348/) (2026)
- [A Unifying Perspective on Probabilities as Model Predictions](https://mlsanity.com/paper/2609.09855/) (2026)
- [Stabilizing Performative Feedback Loops with Minimal Model Deployments](https://mlsanity.com/paper/2609.14065/) (2026)

## Abstract (arXiv)

Calibration means that forecasts and average realized frequencies are close. We develop the concept of forecast hedging, which consists of choosing the forecasts so as to guarantee that the expected track record can only improve. This yields all the calibration results by the same simple basic argument while differentiating between them by the forecast-hedging tools used: deterministic and fixed point based versus stochastic and minimax based. Additional contributions are an improved definition of continuous calibration, ensuing game dynamics that yield Nash equilibria in the long run, and a new calibrated forecasting procedure for binary events that is simpler than all known such procedures.