Conformal risk control for bounded non-monotone losses over a grid of size m achieves excess risk of order sqrt(log m / n) with n calibration samples, which is minimax optimal.
Harris Papadopoulos, Kostas Proedrou, Vladimir Vovk, and Alexander Gammerman
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Conformal Risk Control under Non-Monotone Losses: Theory and Finite-Sample Guarantees
Conformal risk control for bounded non-monotone losses over a grid of size m achieves excess risk of order sqrt(log m / n) with n calibration samples, which is minimax optimal.