We prove the tightest-known upper bounds on the sample complexity of multi-group learning. Our algorithm extends the one-inclusion graph prediction strategy using a generalization of bipartite $b$-matching. In the group-realizable setting, we provide a lower bound confirming that our algorithm's $\log n / n$ convergence rate is optimal in general. If one relaxes the learning objective such that the group on which we are evaluated is chosen obliviously of the sample, then our algorithm achieves the optimal $1/n$ convergence rate under group-realizability.

翻译：我们证明了多组学习样本复杂度的目前最紧上界。我们的算法通过推广二分图$b$-匹配，扩展了单包含图预测策略。在组可实现设定下，我们给出了一个下界，证实了该算法的$\log n / n$收敛速度在一般情况下是最优的。若放宽学习目标，使得我们被评估的组独立于样本随机选择，那么在组可实现性条件下，我们的算法达到了最优的$1/n$收敛速度。