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.

翻译：多任务学习（MTL）旨在通过共享相关任务间的共同信息来提升估计与预测性能。MTL中的一个自然假设是，任务根据其特征被划分为不同的聚类。然而，基于该假设的现有MTL方法常常忽略那些具有较大任务特定成分或与其他任务无关的异常任务。为解决这一问题，我们提出了一种新颖的多任务学习方法，称为基于鲁棒正则化聚类的多任务学习（MTLRRC）。MTLRRC引入了受鲁棒凸聚类启发的鲁棒正则化项，并进一步扩展以处理非凸及群稀疏惩罚。该扩展使得MTLRRC能够同时执行鲁棒的任务聚类与异常任务检测。本文还建立了扩展的鲁棒聚类与多元M估计量之间的联系，从而为MTLRRC对异常任务的鲁棒性提供了一种解释。为估计参数，我们开发了一种基于改进的交替方向乘子法的高效算法。通过模拟研究及实际数据应用，验证了MTLRRC的有效性。