Mixed-integer quadratic programming reformulations of multi-task learning models
In this manuscript, we consider well-known multi-task learning (MTL) models from the literature for linear regression problems, such as clustered MTL or weakly constrained MTL. We propose novel reformulations of the training problem for these models, based on mixed-integer quadratic programming (MIQ...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-03-01
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| Series: | Mathematics in Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mine.2023020?viewType=HTML |
| _version_ | 1827946308373053440 |
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| author | Matteo Lapucci Davide Pucci |
| author_facet | Matteo Lapucci Davide Pucci |
| author_sort | Matteo Lapucci |
| collection | DOAJ |
| description | In this manuscript, we consider well-known multi-task learning (MTL) models from the literature for linear regression problems, such as clustered MTL or weakly constrained MTL. We propose novel reformulations of the training problem for these models, based on mixed-integer quadratic programming (MIQP) techniques. We show that our approach allows to drive the optimization process up to certified global optimality, exploiting popular off-the-shelf software solvers. By computational experiments on both synthetic and real-world datasets, we show that this strategy generally leads to improvements in terms of the predictive performance of the models, if compared to the classical local optimization techniques, based on alternating minimization strategies, that are usually employed. We also suggest a number of possible extensions of our model that should further improve the quality of the obtained regressors, introducing, for example, sparsity and features selection elements. |
| first_indexed | 2024-03-13T10:56:47Z |
| format | Article |
| id | doaj.art-e791ff917259402da3e3ff043df690ba |
| institution | Directory Open Access Journal |
| issn | 2640-3501 |
| language | English |
| last_indexed | 2024-03-13T10:56:47Z |
| publishDate | 2023-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj.art-e791ff917259402da3e3ff043df690ba2023-05-17T01:36:46ZengAIMS PressMathematics in Engineering2640-35012023-03-015111610.3934/mine.2023020Mixed-integer quadratic programming reformulations of multi-task learning modelsMatteo Lapucci 0Davide Pucci1Department of Information Engineering, Università degli Studi di Firenze, Via di Santa Marta 3, 50139 Florence, ItalyDepartment of Information Engineering, Università degli Studi di Firenze, Via di Santa Marta 3, 50139 Florence, ItalyIn this manuscript, we consider well-known multi-task learning (MTL) models from the literature for linear regression problems, such as clustered MTL or weakly constrained MTL. We propose novel reformulations of the training problem for these models, based on mixed-integer quadratic programming (MIQP) techniques. We show that our approach allows to drive the optimization process up to certified global optimality, exploiting popular off-the-shelf software solvers. By computational experiments on both synthetic and real-world datasets, we show that this strategy generally leads to improvements in terms of the predictive performance of the models, if compared to the classical local optimization techniques, based on alternating minimization strategies, that are usually employed. We also suggest a number of possible extensions of our model that should further improve the quality of the obtained regressors, introducing, for example, sparsity and features selection elements.https://www.aimspress.com/article/doi/10.3934/mine.2023020?viewType=HTMLmultitask learningclustered mtlweakly constrained mtlmiqpglobal optimization |
| spellingShingle | Matteo Lapucci Davide Pucci Mixed-integer quadratic programming reformulations of multi-task learning models Mathematics in Engineering multitask learning clustered mtl weakly constrained mtl miqp global optimization |
| title | Mixed-integer quadratic programming reformulations of multi-task learning models |
| title_full | Mixed-integer quadratic programming reformulations of multi-task learning models |
| title_fullStr | Mixed-integer quadratic programming reformulations of multi-task learning models |
| title_full_unstemmed | Mixed-integer quadratic programming reformulations of multi-task learning models |
| title_short | Mixed-integer quadratic programming reformulations of multi-task learning models |
| title_sort | mixed integer quadratic programming reformulations of multi task learning models |
| topic | multitask learning clustered mtl weakly constrained mtl miqp global optimization |
| url | https://www.aimspress.com/article/doi/10.3934/mine.2023020?viewType=HTML |
| work_keys_str_mv | AT matteolapucci mixedintegerquadraticprogrammingreformulationsofmultitasklearningmodels AT davidepucci mixedintegerquadraticprogrammingreformulationsofmultitasklearningmodels |