Omniprediction is a learning problem that requires suboptimality bounds for each of a family of losses $\mathcal{L}$ against a family of comparator predictors $\mathcal{C}$. We initiate the study of omniprediction in a multiclass setting, where the comparator family $\mathcal{C}$ may be infinite. Our main result is an extension of the recent binary omniprediction algorithm of [OKK25] to the multiclass setting, with sample complexity (in statistical settings) or regret horizon (in online settings) $\approx \varepsilon^{-(k+1)}$, for $\varepsilon$-omniprediction in a $k$-class prediction problem. En route to proving this result, we design a framework of potential broader interest for solving Blackwell approachability problems where multiple sets must simultaneously be approached via coupled actions.

翻译：全预测是一种学习问题，要求针对损失函数族 $\mathcal{L}$ 中的每个损失，给出相对于比较器预测器族 $\mathcal{C}$ 的次优性界。我们首次研究了多类设定下的全预测问题，其中比较器族 $\mathcal{C}$ 可能是无限的。我们的主要结果是将近期 [OKK25] 的二元全预测算法推广到多类设定，在统计设定中的样本复杂度或在线设定中的遗憾界约为 $\varepsilon^{-(k+1)}$，用于解决 $k$ 类预测问题中的 $\varepsilon$-全预测。在证明这一结果的过程中，我们设计了一个可能具有更广泛意义的框架，用于解决布莱克韦尔可逼近性问题，其中必须通过耦合动作同时逼近多个集合。