We provide a unifying framework for the design and analysis of multi-calibrated and moment-multi-calibrated predictors. Placing the multi-calibration problem in the general setting of \emph{multi-objective learning} -- where learning guarantees must hold simultaneously over a set of distributions and loss functions -- we exploit connections to game dynamics to obtain state-of-the-art guarantees for a diverse set of multi-calibration learning problems. In addition to shedding light on existing multi-calibration guarantees, and greatly simplifying their analysis, our approach yields a $1/\epsilon^2$ improvement in the number of oracle calls compared to the state-of-the-art algorithm of Jung et al. 2021 for learning deterministic moment-calibrated predictors and an exponential improvement in $k$ compared to the state-of-the-art algorithm of Gopalan et al. 2022 for learning a $k$-class multi-calibrated predictor. Beyond multi-calibration, we use these game dynamics to address existing and emerging considerations in the study of group fairness and multi-distribution learning.

翻译：我们为多校准和矩多校准预测器的设计与分析提供了一个统一框架。将多校准问题置于多目标学习的一般设置中——其中学习保证必须同时在一组分布和损失函数上成立——我们利用博弈动力学的联系，为一系列多样化的多校准学习问题获得了最先进的保证。除了阐明现有的多校准保证并大幅简化其分析外，我们的方法在确定性矩校准预测器的学习中将预言调用次数相比Jung等人（2021）的最先进算法提升了1/ε²，且在k类多校准预测器的学习中将复杂度相比Gopalan等人（2022）的最先进算法在k上实现了指数级改进。超越多校准本身，我们使用这些博弈动力学来解决群体公平性和多分布学习研究中现有及新兴的考量。