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

TL;DR

This paper introduces a unifying game-theoretic framework for multicalibration in multi-objective learning, leading to improved guarantees and simplified analysis across diverse fairness and distributional settings.

Contribution

It provides a novel game dynamics approach that unifies and enhances multicalibration guarantees, simplifying analysis and extending to fairness and multi-distribution learning.

Findings

Achieves stronger multicalibration conditions scaling with group size

Reduces complexity of k-class multicalibration exponentially

Provides a unified framework simplifying existing guarantees

Abstract

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.