  Multitask learning aims at solving a set of related tasks simultaneously, by
exploiting the shared knowledge for improving the performance on individual
tasks. Hence, an important aspect of multitask learning is to understand the
similarities within a set of tasks. Previous works have incorporated this
similarity information explicitly (e.g., weighted loss for each task) or
implicitly (e.g., adversarial loss for feature adaptation), for achieving good
empirical performances. However, the theoretical motivations for adding task
similarity knowledge are often missing or incomplete. In this paper, we give a
different perspective from a theoretical point of view to understand this
practice. We first provide an upper bound on the generalization error of
multitask learning, showing the benefit of explicit and implicit task
similarity knowledge. We systematically derive the bounds based on two distinct
task similarity metrics: H divergence and Wasserstein distance. From these
theoretical results, we revisit the Adversarial Multi-task Neural Network,
proposing a new training algorithm to learn the task relation coefficients and
neural network parameters iteratively. We assess our new algorithm empirically
on several benchmarks, showing not only that we find interesting and robust
task relations, but that the proposed approach outperforms the baselines,
reaffirming the benefits of theoretical insight in algorithm design.
