Multi-task Highly Adaptive Lasso
This addresses multi-task learning problems for researchers and practitioners by providing a novel nonparametric method with strong theoretical guarantees and empirical performance.
The authors tackled the problem of multi-task learning by proposing MT-HAL, a fully nonparametric approach that simultaneously learns features, samples, and task associations with shared sparse structure, achieving a dimension-free convergence rate of o_p(n^{-1/4}) or better and outperforming sparsity-based competitors in simulations.
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.