Multi-task learning (MTL) aims to improve estimation and prediction
performance by sharing common information among related tasks. One natural
assumption in MTL is that tasks are classified into clusters based on their
characteristics. However, existing MTL methods based on this assumption often
ignore outlier tasks that have large task-specific components or no relation to
other tasks. To address this issue, we propose a novel MTL method called
Multi-Task Learning via Robust Regularized Clustering (MTLRRC). MTLRRC
incorporates robust regularization terms inspired by robust convex clustering,
which is further extended to handle non-convex and group-sparse penalties. The
extension allows MTLRRC to simultaneously perform robust task clustering and
outlier task detection. The connection between the extended robust clustering
and the multivariate M-estimator is also established. This provides an
interpretation of the robustness of MTLRRC against outlier tasks. An efficient
algorithm based on a modified alternating direction method of multipliers is
developed for the estimation of the parameters. The effectiveness of MTLRRC is
demonstrated through simulation studies and application to real data.

多任务学习通过鲁棒正则化聚类（MTLRRC）方法，同时进行鲁棒任务聚类和异常任务检测，提高估计和预测性能。

基于鲁棒正则聚类和非凸群体惩罚的多任务学习

Multi-task learning via robust regularized clustering with non-convex  group penalties

Multi-task learning is a learning paradigm which seeks to improve the
generalization performance of a learning task with the help of some other
related tasks. In this paper, we propose a regularization formulation for
learning the relationships between tasks in multi-task learning. This
formulation can be viewed as a novel generalization of the regularization
framework for single-task learning. Besides modeling positive task correlation,
our method, called multi-task relationship learning (MTRL), can also describe
negative task correlation and identify outlier tasks based on the same
underlying principle. Under this regularization framework, the objective
function of MTRL is convex. For efficiency, we use an alternating method to
learn the optimal model parameters for each task as well as the relationships
between tasks. We study MTRL in the symmetric multi-task learning setting and
then generalize it to the asymmetric setting as well. We also study the
relationships between MTRL and some existing multi-task learning methods.
Experiments conducted on a toy problem as well as several benchmark data sets
demonstrate the effectiveness of MTRL.

提出了一种正则化公式，用于在多任务学习中学习任务之间的关系，可以对正相关、负相关和异常任务进行建模，在对称和非对称多任务学习设置下，使用交替优化算法， 对模型参数和任务之间的关系进行优化。实验结果表明这种方法的有效性。