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

Nika Haghtalab · Michael Jordan · Eric Zhao

Great Hall & Hall B1+B2 (level 1) #1805
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Tue 12 Dec 8:45 a.m. PST — 10:45 a.m. PST

Abstract: We provide a unifying framework for the design and analysis of multi-calibrated predictors. By placing the multi-calibration 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 multi-calibration learning problems. In addition to shedding light on existing multi-calibration guarantees and greatly simplifying their analysis, our approach also yields improved guarantees, such as error tolerances that scale with the square-root of group size versus the constant tolerances guaranteed by prior works, and improving the complexity of $k$-class multi-calibration by an exponential factor of $k$ versus Gopalan et al.. Beyond multi-calibration, we use these game dynamics to address emerging considerations in the study of group fairness and multi-distribution learning.

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