A Principled Approach for Learning Task Similarity in Multitask Learning

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

Wasserstein regularization for sparse multi-task regression

International audienceWe focus in this paper on high-dimensional regression problems where each regressor can be associated to a location in a physical space, or more generally a generic geometric space. Such problems often employ sparse priors, which promote models using a small subset of regressors. To increase statistical power, the so-called multi-task techniques were proposed, which consist in the simultaneous estimation of several related models. Combined with sparsity assumptions, it lead to models enforcing the active regressors to be shared across models, thanks to, for instance L1 / Lq norms. We argue in this paper that these techniques fail to leverage the spatial information associated to regressors. Indeed, while sparse priors enforce that only a small subset of variables is used, the assumption that these regressors overlap across all tasks is overly simplistic given the spatial variability observed in real data. In this paper, we propose a convex reg-ularizer for multi-task regression that encodes a more flexible geometry. Our regularizer is based on unbalanced optimal transport (OT) theory, and can take into account a prior geometric knowledge on the regressor variables, without necessarily requiring overlapping supports. We derive an efficient algorithm based on a regularized formulation of OT, which iterates through applications of Sinkhorn's algorithm along with coordinate descent iterations. The performance of our model is demonstrated on regular grids with both synthetic and real datasets as well as complex triangulated geometries of the cortex with an application in neuroimaging