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

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.