A latest line of labor reveals that notions of multigroup equity suggest surprisingly robust notions of omniprediction: loss minimization ensures that apply not only for a selected loss perform, however for any loss belonging to a big household of losses. Whereas prior work has derived numerous notions of omniprediction from multigroup equity ensures of various power, it was unknown whether or not the connection goes in each instructions. On this work, we reply this query within the affirmative, establishing equivalences between notions of multicalibration and omniprediction. The brand new definitions that maintain the important thing to this equivalence are new notions of swap omniprediction, that are impressed by swap remorse in on-line studying. We present that these will be characterised precisely by a strengthening of multicalibration that we discuss with as swap multicalibration. One can go from commonplace to swap multicalibration by a easy discretization; furthermore all recognized algorithms for normal multicalibration the truth is give swap multicalibration. Within the context of omniprediction although, introducing the notion of swapping leads to provably stronger notions, which require a predictor to reduce anticipated loss at the least in addition to an adaptive adversary who can select each the loss perform and speculation based mostly on the worth predicted by the predictor.
Constructing on these characterizations, we paint an entire image of the connection between the assorted omniprediction notions within the literature by establishing implications and separations between them. Our work deepens our understanding of the connections between multigroup equity, loss minimization and consequence indistinguishability and establishes new connections to basic notions in on-line studying.