We propose a novel, fully nonparametric approach for the multi-task learning, the Multi-task Highly Adaptive Lasso (MT-HAL). MT-HAL simultaneously learns features, samples and task associations important for the common model, while imposing a shared sparse structure among similar tasks. Given multiple tasks, our approach automatically finds a sparse sharing structure. The proposed MTL algorithm attains a powerful dimension-free convergence rate of $o_p(n^{-1/4})$ or better. We show that MT-HAL outperforms sparsity-based MTL competitors across a wide range of simulation studies, including settings with nonlinear and linear relationships, varying levels of sparsity and task correlations, and different numbers of covariates and sample size.

翻译：本文提出了一种全新的完全非参数化多任务学习方法——多任务高适应性Lasso（MT-HAL）。MT-HAL能同时学习对共同模型具有重要意义的特征、样本和任务关联性，同时为相似任务施加共享稀疏结构。在给定多个任务的情况下，该方法可自动发现稀疏共享结构。所提出的多任务学习算法实现了强大的维度无关收敛速率$o_p(n^{-1/4})$甚至更优。研究表明，在涵盖非线性与线性关系、不同稀疏度与任务相关性水平、以及不同协变量数量与样本量的广泛模拟场景中，MT-HAL均优于基于稀疏性的多任务学习竞争方法。