  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.
