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 multiobjective
learning—where learning guarantees must hold simultaneously over a set of distribu-
tions 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 ap-
proach yields a 1/ε2 improvement in the number of oracle calls compared to the state-of-the-art
algorithm of Jung et al. [19] for learning deterministic moment-calibrated predictors and an
exponential improvement in k compared to the state-of-the-art algorithm of Gopalan et al. [14]
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.
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A Unifying Perspective on Multi-Calibration: Game Dynamics for Multi-Objective Learning
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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« less
- Award ID(s):
- 2145898
- PAR ID:
- 10494288
- Publisher / Repository:
- Advances in Neural Information Processing Systems 36 (NeurIPS 2023)
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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