Multicalibration has minimax sample complexity Θ̃(ε^{-3}) when the number of groups is at most ε^{-κ} for fixed κ>0, versus Θ̃(ε^{-2}) for marginal calibration, with a sharp threshold at κ=0.
Pai, and Aaron Roth
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The Sample Complexity of Multicalibration
Multicalibration has minimax sample complexity Θ̃(ε^{-3}) when the number of groups is at most ε^{-κ} for fixed κ>0, versus Θ̃(ε^{-2}) for marginal calibration, with a sharp threshold at κ=0.