Multigroup Fairness and Omniprediction: Separations and Equivalences

Omniprediction [GKR+22] is a powerful learning guarantee that requires a predictor to be competitive with the best hypothesis from a benchmark class, not just for a single loss function, but simultaneously across all loss functions in a prespecified family. Currently, learning algorithms for achieving omniprediction rely on notions of multigroup fairness, such as multiaccuracy and multicalibration [HKRR18] or calibrated multiaccuracy [GHK+23]. In this work, we ask whether this reliance is necessary: Does omniprediction require some form of multigroup fairness? We answer this question in the negative. While prior works have shown that various multigroup fairness notions imply omniprediction [GKR+22, GHK+23, OKK25], we rule out even a weak converse. Specifically, we show that omniprediction for proper losses does not even require accuracy in expectation, a much weaker notion than calibration or multiaccuracy. We complement our negative answer for omniprediction with an affirmative answer for loss outcome indistinguishability (loss OI) [GHK+23], a related but stronger learning guarantee. Loss OI, which implies omniprediction, requires the predicted label distribution to be indistinguishable from the true label distribution by a certain class of tests depending on the loss functions and the benchmark class. Prior work showed how to achieve loss OI from a combination of calibration and multiaccuracy [GHK+23]. We prove the converse, establishing that loss OI is in fact equivalent to a form of calibrated multiaccuracy.