# Smooth Calibration and Decision Making

arXiv: https://arxiv.org/abs/2504.15582 · HTML: https://mlsanity.com/paper/2504.15582/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 29 references that are in the map.
- First posted on arXiv 22 Apr 2025.

## Builds on (most cited first, 16 of 16)

- [Multiaccuracy: Black-Box Post-Processing for Fairness in Classification](https://mlsanity.com/paper/1805.12317/) (2018)
- [Omnipredictors](https://mlsanity.com/paper/2109.05389/) (2021)
- [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)
- [Stronger Calibration Lower Bounds via Sidestepping](https://mlsanity.com/paper/2012.03454/) (2020)
- [Oracle Efficient Online Multicalibration and Omniprediction](https://mlsanity.com/paper/2307.08999/) (2023)
- [When Does Optimizing a Proper Loss Yield Calibration?](https://mlsanity.com/paper/2305.18764/) (2023)
- [Swap Agnostic Learning, or Characterizing Omniprediction via Multicalibration](https://mlsanity.com/paper/2302.06726/) (2023)
- [Smooth Calibration, Leaky Forecasts, Finite Recall, and Nash Dynamics](https://mlsanity.com/paper/2210.07152/) (2022)
- [On the Distance from Calibration in Sequential Prediction](https://mlsanity.com/paper/2402.07458/) (2024)
- [Breaking the T2/3 Barrier for Sequential Calibration](https://mlsanity.com/paper/2406.13668/) (2024)
- [Omnipredictors for Regression and the Approximate Rank of Convex Functions](https://mlsanity.com/paper/2401.14645/) (2024)
- [Omnipredictors for Constrained Optimization](https://mlsanity.com/paper/2209.07463/) (2022)
- [From External to Swap Regret 2.0: An Efficient Reduction and Oblivious Adversary for Large Action Spaces](https://mlsanity.com/paper/2310.19786/) (2023)
- [Truthfulness of Calibration Measures](https://mlsanity.com/paper/2407.13979/) (2024)

## Built on by (most cited first, 10 of 10)

- [Calibration through the Lens of Indistinguishability](https://mlsanity.com/paper/2509.02279/) (2025)
- [Efficient Calibration for Decision Making](https://mlsanity.com/paper/2511.13699/) (2025)
- [Forecast Skill Is Not Decision Skill: Evidence from Weather-Dependent Decision Tasks](https://mlsanity.com/paper/2512.14779/) (2025)
- [The Importance of Being Smoothly Calibrated](https://mlsanity.com/paper/2603.16015/) (2026)
- [Testable and Actionable Calibration for Full Swap Regret](https://mlsanity.com/paper/2605.17749/) (2026)
- [Computational and Statistical Hardness of Calibration Distance](https://mlsanity.com/paper/2603.18391/) (2026)
- [Smoothed Elicitation Complexity for Approximate Gamma-calibration of Discrete Classification Tasks](https://mlsanity.com/paper/2605.23017/) (2026)
- [Decision-Aware Training for Sample-Based Generative Models](https://mlsanity.com/paper/2607.01171/) (2026)
- [Truthful Calibration Measures for Sequential Prediction](https://mlsanity.com/paper/2608.21348/) (2026)
- [Sharp Integrality Gaps in Calibration Distance](https://mlsanity.com/paper/2610.05679/) (2026)

## Abstract (arXiv)

Calibration requires predictor outputs to be consistent with their Bayesian posteriors. For machine learning predictors that do not distinguish between small perturbations, calibration errors are continuous in predictions, e.g., smooth calibration error (Foster and Hart, 2018), Distance to Calibration (Blasiok et al., 2023a). On the contrary, decision-makers who use predictions make optimal decisions discontinuously in probabilistic space, experiencing loss from miscalibration discontinuously. Calibration errors for decision-making are thus discontinuous, e.g., Expected Calibration Error (Foster and Vohra, 1997), and Calibration Decision Loss (Hu and Wu, 2024). Thus, predictors with a low calibration error for machine learning may suffer a high calibration error for decision-making, i.e., they may not be trustworthy for decision-makers optimizing assuming their predictions are correct. It is natural to ask if post-processing a predictor with a low calibration error for machine learning is without loss to achieve a low calibration error for decision-making. In our paper, we show that post-processing an online predictor with ε distance to calibration achieves O(√ε) ECE and CDL, which is asymptotically optimal. The post-processing algorithm adds noise to make predictions differentially private. The optimal bound from low distance to calibration predictors from post-processing is non-optimal compared with existing online calibration algorithms that directly optimize for ECE and CDL.