Adaptive sieving with semismooth Newton proximal augmented Lagrangian algorithm for multi-task Lasso problems

2025/04/21 by Lin, Lanyu, Liu, Yong-Jin, Wang, Bo +1
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2504.15113

Abstract

Multi-task learning enhances model generalization by jointly learning from related tasks. This paper focuses on the ℓ_1,∞-norm constrained multi-task learning problem, which promotes a shared feature representation while inducing sparsity in task-specific parameters. We propose an adaptive sieving (AS) strategy to efficiently generate a solution path for multi-task Lasso problems. Each subproblem along the path is solved via an inexact semismooth Newton proximal augmented Lagrangian (\sc Ssnpal) algorithm, achieving an asymptotically superlinear convergence rate. By exploiting the Karush-Kuhn-Tucker (KKT) conditions and the inherent sparsity of multi-task Lasso solutions, the \sc Ssnpal algorithm solves a sequence of reduced subproblems with small dimensions. This approach enables our method to scale effectively to large problems. Numerical experiments on synthetic and real-world datasets demonstrate the superior efficiency and robustness of our algorithm compared to state-of-the-art solvers.

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