An Efficient Augmented Lagrangian Based Method for Constrained Lasso
This work addresses the need for faster and more accurate variable selection in statistics and machine learning, though it appears incremental as it builds on existing constrained Lasso models.
The authors tackled the constrained Lasso problem by developing an inexact augmented Lagrangian method that exploits second-order sparsity, resulting in superior computational efficiency and solution accuracy compared to existing first-order methods, as demonstrated on synthetic and real data.
Variable selection is one of the most important tasks in statistics and machine learning. To incorporate more prior information about the regression coefficients, the constrained Lasso model has been proposed in the literature. In this paper, we present an inexact augmented Lagrangian method to solve the Lasso problem with linear equality constraints. By fully exploiting second-order sparsity of the problem, we are able to greatly reduce the computational cost and obtain highly efficient implementations. Furthermore, numerical results on both synthetic data and real data show that our algorithm is superior to existing first-order methods in terms of both running time and solution accuracy.