Adaptive sieving with semismooth Newton proximal augmented Lagrangian algorithm for multi-task Lasso problems
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915252166197248 |
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| author | Lin, Lanyu Liu, Yong-Jin Wang, Bo Yang, Junfeng |
| author_facet | Lin, Lanyu Liu, Yong-Jin Wang, Bo Yang, Junfeng |
| contents | Multi-task learning enhances model generalization by jointly learning from related tasks. This paper focuses on the $\ell_{1,\infty}$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15113 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adaptive sieving with semismooth Newton proximal augmented Lagrangian algorithm for multi-task Lasso problems Lin, Lanyu Liu, Yong-Jin Wang, Bo Yang, Junfeng Optimization and Control Multi-task learning enhances model generalization by jointly learning from related tasks. This paper focuses on the $\ell_{1,\infty}$-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. |
| title | Adaptive sieving with semismooth Newton proximal augmented Lagrangian algorithm for multi-task Lasso problems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2504.15113 |