Paper shows swap agnostic learning is equivalent to multicalibration and omniprediction
Sauers_ · x · 2026-08-04
What the paper claims
The paper introduces Swap Agnostic Learning (SAL), framed as a game between a predictor and an adversary. The predictor picks a hypothesis, the adversary responds, and the predictor is considered successful if its hypothesis competes with the adversary’s loss across all level sets.
Main result
The authors show that SAL is feasible for any convex loss. The proof comes from connecting three notions:
- Omniprediction
- Multicalibration
- Swap variants of both ideas
They show that swap omniprediction and multicalibration are equivalent to SAL, and that swap multicalibration is essentially equivalent to standard multicalibration, so existing learning algorithms can achieve all three notions.
Broader implication
The paper also maps out the relationship between:
- multi-group fairness
- omniprediction
- outcome indistinguishability
That yields a unified view of outcome indistinguishability that captures the existing omniprediction and multicalibration frameworks.
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