We consider the problem of learning multioutput function classes in batch and online settings. In both settings, we show that a multioutput function class is learnable if and only if each single-output restriction of the function class is learnable. This provides a complete characterization of the learnability of multilabel classification and multioutput regression in both batch and online settings. As an extension, we also consider multilabel learnability in the bandit feedback setting and show a similar characterization as in the full-feedback setting.

翻译：我们研究了批量和在线设置下多输出函数类的学习问题。在两种设置中，我们证明：一个多输出函数类是可学习的，当且仅当该函数类的每个单输出限制都是可学习的。这为批量与在线设置下的多标签分类和多输出回归提供了可学习性的完整刻画。作为扩展，我们还考虑了强盗反馈设置下的多标签可学习性，并展示了与全反馈设置相似的刻画结果。