A Characterization of Multilabel Learnability

We consider the problem of multilabel classification and investigate learnability in batch and online settings. In both settings, we show that a multilabel function class is learnable if and only if each single-label restriction of the function class is learnable. As extensions, we also study multioutput regression in the batch setting and bandit feedback in the online setting. For the former, we characterize learnability w.r.t. $L_p$ losses. For the latter, we show a similar characterization as in the full-feedback setting.