# Smooth Calibration, Leaky Forecasts, Finite Recall, and Nash Dynamics

arXiv: https://arxiv.org/abs/2210.07152 · HTML: https://mlsanity.com/paper/2210.07152/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 34 references that are in the map.
- First posted on arXiv 13 Oct 2022.

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

- [Relative Loss Bounds for On-line Density Estimation with the Exponential Family of Distributions](https://mlsanity.com/paper/1301.6677/) (2013)

## 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)
- [Forecasting for Swap Regret for All Downstream Agents](https://mlsanity.com/paper/2402.08753/) (2024)
- [On Computationally Efficient Multi-Class Calibration](https://mlsanity.com/paper/2402.07821/) (2024)
- [Fair Risk Control: A Generalized Framework for Calibrating Multi-group Fairness Risks](https://mlsanity.com/paper/2405.02225/) (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)
- [Smooth Calibration and Decision Making](https://mlsanity.com/paper/2504.15582/) (2025)
- [How Flawed Is ECE? An Analysis via Logit Smoothing](https://mlsanity.com/paper/2402.10046/) (2024)
- [Pseudonorm Approachability and Applications to Regret Minimization](https://mlsanity.com/paper/2302.01517/) (2023)
- [Three Types of Calibration with Properties and their Semantic and Formal Relationships](https://mlsanity.com/paper/2504.18395/) (2025)
- [Rate-Preserving Reductions for Blackwell Approachability](https://mlsanity.com/paper/2406.07585/) (2024)
- [Learning and Computation of Phi-Equilibria at the Frontier of Tractability](https://mlsanity.com/paper/2502.18582/) (2025)
- [Set Learning for Accurate and Calibrated Models](https://mlsanity.com/paper/2307.02245/) (2023)
- [An Elementary Predictor Obtaining 2√T+1 Distance to Calibration](https://mlsanity.com/paper/2402.11410/) (2024)
- [Instance-Adaptive Online Multicalibration](https://mlsanity.com/paper/2605.09273/) (2026)
- [Proper Calibeating](https://mlsanity.com/paper/2605.26703/) (2026)
- [Uniform convergence of the smooth calibration error and its relationship with functional gradient](https://mlsanity.com/paper/2505.19396/) (2025)
- [Decision Making under Imperfect Recall: Algorithms and Benchmarks](https://mlsanity.com/paper/2602.15252/) (2026)
- [Regret, equilibrium, and learning in games: A guided tour](https://mlsanity.com/paper/2608.09389/) (2026)

## Abstract (arXiv)

We propose to smooth out the calibration score, which measures how good a forecaster is, by combining nearby forecasts. While regular calibration can be guaranteed only by randomized forecasting procedures, we show that smooth calibration can be guaranteed by deterministic procedures. As a consequence, it does not matter if the forecasts are leaked, i.e., made known in advance: smooth calibration can nevertheless be guaranteed (while regular calibration cannot). Moreover, our procedure has finite recall, is stationary, and all forecasts lie on a finite grid. To construct the procedure, we deal also with the related setups of online linear regression and weak calibration. Finally, we show that smooth calibration yields uncoupled finite-memory dynamics in n-person games "smooth calibrated learning" in which the players play approximate Nash equilibria in almost all periods (by contrast, calibrated learning, which uses regular calibration, yields only that the time-averages of play are approximate correlated equilibria).