We discuss a general method to learn data representations from multiple
tasks. We provide a justification for this method in both settings of multitask
learning and learning-to-learn. The method is illustrated in detail in the
special case of linear feature learning. Conditions on the theoretical
advantage offered by multitask representation learning over independent task
learning are established. In particular, focusing on the important example of
half-space learning, we derive the regime in which multitask representation
learning is beneficial over independent task learning, as a function of the
sample size, the number of tasks and the intrinsic data dimensionality. Other
potential applications of our results include multitask feature learning in
reproducing kernel Hilbert spaces and multilayer, deep networks.

讨论了一般从多个任务中学习数据表示的方法，并在多任务学习和学习到学习的两种情况下对此方法进行了理论上的证明。我们通过线性特征学习的特例对方法进行详细说明，并建立起多任务表示学习在独立任务学习上的理论优势的条件，特别是针对重要的半空间学习的例子，我们推导出了多任务表示学习在独立任务学习上的优势随样本数量、任务数量和固有数据维度的函数关系，其他潜在应用包括在再现核希尔伯特空间和多层深度网络中进行多任务特征学习。