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。在这两种设置中，我们证明了多输出函数类的可学习性当且仅当该函数类的每个单输出限制是可学习的。这为批量和在线设置下的多标签分类和多输出回归的可学习性提供了完整的刻画。作为扩展，我们还考虑了赌博反馈设置下的多标签可学习性，并展示了与全反馈设置类似的刻画。