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A recent line of work has shown a surprising connection betweenmulticalibration, a multi-group fairness notion, and omniprediction, a learningparadigm that provides simultaneous loss minimization guarantees for a largefamily of loss functions. Prior work studies omniprediction in the batchsetting. We initiate the study of omniprediction in the online adversarialsetting. Although there exist algorithms for obtaining notions ofmulticalibration in the online adversarial setting, unlike batch algorithms,they work only for small finite classes of benchmark functions $F$, becausethey require enumerating every function $f \in F$ at every round. In contrast,omniprediction is most interesting for learning theoretic hypothesis classes$F$, which are generally continuously large.  We develop a new online multicalibration algorithm that is well defined forinfinite benchmark classes $F$, and is oracle efficient (i.e. for any class$F$, the algorithm has the form of an efficient reduction to a no-regretlearning algorithm for $F$). The result is the first efficient onlineomnipredictor -- an oracle efficient prediction algorithm that can be used tosimultaneously obtain no regret guarantees to all Lipschitz convex lossfunctions. For the class $F$ of linear functions, we show how to make ouralgorithm efficient in the worst case. Also, we show upper and lower bounds onthe extent to which our rates can be improved: our oracle efficient algorithmactually promises a stronger guarantee called swap-omniprediction, and we provea lower bound showing that obtaining $O(\sqrt{T})$ bounds forswap-omniprediction is impossible in the online setting. On the other hand, wegive a (non-oracle efficient) algorithm which can obtain the optimal$O(\sqrt{T})$ omniprediction bounds without going through multicalibration,giving an information theoretic separation between these two solution concepts.

Oracle Efficient Online Multicalibration and Omniprediction