A Characterization of Multioutput Learnability

TL;DR

This paper provides a complete characterization of when multioutput function classes are learnable in batch, online, and bandit feedback settings, based on the learnability of their single-output restrictions.

Contribution

It establishes that multioutput learnability is equivalent to the learnability of all single-output restrictions across various learning settings.

Findings

Multioutput learnability is characterized by single-output learnability.

The characterization applies to batch, online, and bandit feedback settings.

Provides a unified framework for multilabel and multioutput regression learning.

Abstract

We consider the problem of learning multioutput function classes in the 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.