A recent line of work has shown a surprising connection between multicalibration, a multi-group fairness notion, and omniprediction, a learning paradigm that provides simultaneous loss minimization guarantees for a large family of loss functions. Prior work studies omniprediction in the batch setting. We initiate the study of omniprediction in the online adversarial setting. Although there exist algorithms for obtaining notions of multicalibration in the online adversarial setting, unlike batch algorithms, they work only for small finite classes of benchmark functions $F$, because they 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 for infinite 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-regret learning algorithm for $F$). The result is the first efficient online omnipredictor -- an oracle efficient prediction algorithm that can be used to simultaneously obtain no regret guarantees to all Lipschitz convex loss functions. For the class $F$ of linear functions, we show how to make our algorithm efficient in the worst case. Also, we show upper and lower bounds on the extent to which our rates can be improved: our oracle efficient algorithm actually promises a stronger guarantee called swap-omniprediction, and we prove a lower bound showing that obtaining $O(\sqrt{T})$ bounds for swap-omniprediction is impossible in the online setting. On the other hand, we give 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.

翻译：近期的系列研究揭示了多重校准（一种多组公平性概念）与全预测（一种可为大规模损失函数族同时提供损失最小化保证的学习范式）之间的惊人联系。先前的工作在批处理设置下研究了全预测。我们率先在在线对抗性设置下研究全预测。尽管已有算法能在在线对抗性设置下获得多重校准的概念，但与批处理算法不同，这些算法仅适用于有限小类基准函数$F$，因为它们需要在每一轮枚举每个函数$f \in F$。相比之下，全预测对于学习理论假设类$F$（通常为连续大规模）更具研究价值。我们提出了一种新的在线多重校准算法，该算法对无限基准函数类$F$定义明确，且具有oracle高效性（即：对于任意函数类$F$，该算法可高效归约为针对$F$的无遗憾学习算法）。这一成果催生了首个高效在线全预测器——一种oracle高效预测算法，可用于同时为所有Lipschitz凸损失函数提供无遗憾保证。针对线性函数类$F$，我们展示了如何在最坏情况下实现算法的高效性。此外，我们给出了关于算法优化速率上下界的理论分析：我们的oracle高效算法实际上提供了更强的交换全预测保证，但我们证明在在线设置下无法获得$O(\sqrt{T})$界的交换全预测。另一方面，我们提出了一种（非oracle高效）算法，该算法无需通过多重校准即可获得最优的$O(\sqrt{T})$全预测界，这揭示了这两种解概念之间存在信息论层面的分离。