# A Unifying Perspective on Multi-Calibration: Game Dynamics for Multi-Objective Learning

arXiv: https://arxiv.org/abs/2302.10863 · HTML: https://mlsanity.com/paper/2302.10863/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 39 references that are in the map.
- First posted on arXiv 21 Feb 2023.

## Builds on (most cited first, 18 of 18)

- [Agnostic Federated Learning](https://mlsanity.com/paper/1902.00146/) (2019)
- [Multiaccuracy: Black-Box Post-Processing for Fairness in Classification](https://mlsanity.com/paper/1805.12317/) (2018)
- [Strongly Adaptive Online Learning](https://mlsanity.com/paper/1502.07073/) (2015)
- [A Second-order Bound with Excess Losses](https://mlsanity.com/paper/1402.2044/) (2014)
- [Algorithmic Stability for Adaptive Data Analysis](https://mlsanity.com/paper/1511.02513/) (2015)
- [Outcome Indistinguishability](https://mlsanity.com/paper/2011.13426/) (2020)
- [Omnipredictors](https://mlsanity.com/paper/2109.05389/) (2021)
- [Batch Multivalid Conformal Prediction](https://mlsanity.com/paper/2209.15145/) (2022)
- [Practical Adversarial Multivalid Conformal Prediction](https://mlsanity.com/paper/2206.01067/) (2022)
- [Moment Multicalibration for Uncertainty Estimation](https://mlsanity.com/paper/2008.08037/) (2020)
- [Online Multivalid Learning: Means, Moments, and Prediction Intervals](https://mlsanity.com/paper/2101.01739/) (2021)
- [Low-Degree Multicalibration](https://mlsanity.com/paper/2203.01255/) (2022)
- [Multi-group Agnostic PAC Learnability](https://mlsanity.com/paper/2105.09989/) (2021)
- [On-Demand Sampling: Learning Optimally from Multiple Distributions](https://mlsanity.com/paper/2210.12529/) (2022)
- [Advancing subgroup fairness via sleeping experts](https://mlsanity.com/paper/1909.08375/) (2019)
- [Simple and near-optimal algorithms for hidden stratification and multi-group learning](https://mlsanity.com/paper/2112.12181/) (2021)
- [Sample Complexity of Uniform Convergence for Multicalibration](https://mlsanity.com/paper/2005.01757/) (2020)
- [Calibrated Forecasts: The Minimax Proof](https://mlsanity.com/paper/2209.05863/) (2022)

## Built on by (most cited first, 30 of 30)

- [High-Dimensional Prediction for Sequential Decision Making](https://mlsanity.com/paper/2310.17651/) (2023)
- [When is Multicalibration Post-Processing Necessary?](https://mlsanity.com/paper/2406.06487/) (2024)
- [Optimal Multi-Distribution Learning](https://mlsanity.com/paper/2312.05134/) (2023)
- [Group-wise oracle-efficient algorithms for online multi-group learning](https://mlsanity.com/paper/2406.05287/) (2024)
- [Generalized Venn and Venn-Abers Calibration with Applications in Conformal Prediction](https://mlsanity.com/paper/2502.05676/) (2025)
- [Discretization-free Multicalibration through Loss Minimization over Tree Ensembles](https://mlsanity.com/paper/2505.17435/) (2025)
- [Fairness-Aware Estimation of Graphical Models](https://mlsanity.com/paper/2408.17396/) (2024)
- [MCGrad: Multicalibration at Web Scale](https://mlsanity.com/paper/2509.19884/) (2025)
- [Efficient Swap Multicalibration of Elicitable Properties](https://mlsanity.com/paper/2511.04907/) (2025)
- [Improved Bounds for Swap Multicalibration and Swap Omniprediction](https://mlsanity.com/paper/2505.20885/) (2025)
- [Measuring multi-calibration](https://mlsanity.com/paper/2506.11251/) (2025)
- [Panprediction: Optimal Predictions for Any Downstream Task and Loss](https://mlsanity.com/paper/2510.27638/) (2025)
- [Learning With Multi-Group Guarantees For Clusterable Subpopulations](https://mlsanity.com/paper/2410.14588/) (2024)
- [Group-realizable multi-group learning by minimizing empirical risk](https://mlsanity.com/paper/2601.16922/) (2026)
- [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)
- [Multicalibration Yields Better Matchings](https://mlsanity.com/paper/2511.11413/) (2025)
- [Near-optimal Swap Regret Minimization for Convex Losses](https://mlsanity.com/paper/2602.08862/) (2026)
- [Optimal Deterministic Multicalibration and Omniprediction](https://mlsanity.com/paper/2606.20557/) (2026)
- [Learning Pareto manifolds in high dimensions: How can regularization help?](https://mlsanity.com/paper/2503.08849/) (2025)
- [Sample-efficient Multiclass Calibration under ℓp Error](https://mlsanity.com/paper/2509.23000/) (2025)
- [Sample-Adaptivity Tradeoff in On-Demand Sampling](https://mlsanity.com/paper/2511.15507/) (2025)
- [On the Convergence of Multicalibration Gradient Boosting](https://mlsanity.com/paper/2602.06773/) (2026)
- [Instance-Adaptive Online Multicalibration](https://mlsanity.com/paper/2605.09273/) (2026)
- [The price of multi-group transductive learning](https://mlsanity.com/paper/2606.04423/) (2026)
- [Learning in Repeated Multi-Objective Stackelberg Games with Payoff Manipulation](https://mlsanity.com/paper/2508.14705/) (2025)
- [Auditability and the Landscape of Distance to Multicalibration](https://mlsanity.com/paper/2509.16930/) (2025)
- [Locally Adaptive Multi-Objective Learning](https://mlsanity.com/paper/2602.14952/) (2026)
- [ShakyPrepend: A Multi-Group Learner with Improved Sample Complexity](https://mlsanity.com/paper/2603.07319/) (2026)
- [Blackwell Approachability and Gradient Equilibrium are Equivalent](https://mlsanity.com/paper/2606.27315/) (2026)
- [Sample-Optimal Multi-Group Learning with an ERM Oracle](https://mlsanity.com/paper/2610.15916/) (2026)

## Abstract (arXiv)

We provide a unifying framework for the design and analysis of multicalibrated predictors. By placing the multicalibration problem in the general setting of multi-objective learning -- where learning guarantees must hold simultaneously over a set of distributions and loss functions -- we exploit connections to game dynamics to achieve state-of-the-art guarantees for a diverse set of multicalibration learning problems. In addition to shedding light on existing multicalibration guarantees and greatly simplifying their analysis, our approach also yields improved guarantees, such as obtaining stronger multicalibration conditions that scale with the square-root of group size and improving the complexity of k-class multicalibration by an exponential factor of k. Beyond multicalibration, we use these game dynamics to address emerging considerations in the study of group fairness and multi-distribution learning.