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...

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Veröffentlicht in:Mathematics in engineering Jg. 5; H. 1; S. 1 - 16
Hauptverfasser: Lapucci, Matteo, Pucci, Davide
Format: Journal Article
Sprache:Englisch
Veröffentlicht: AIMS Press 01.03.2023
Schlagworte:
clustered mtl
global optimization
miqp
multitask learning
weakly constrained mtl
ISSN:2640-3501, 2640-3501
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Abstract 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.
AbstractList 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.
Author Lapucci, Matteo
Pucci, Davide
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Cites_doi 10.1609/aaai.v29i1.9581
10.1609/aaai.v27i1.8577
10.1145/1645953.1646169
10.1214/16-STS602
10.1109/ICCV.2011.6126288
10.1007/s10589-019-00134-5
10.1561/9781601984616
10.1145/2538028
10.1145/2556195.2556264
10.1145/2020408.2020423
10.1016/j.ejor.2015.06.081
10.1109/ICCV.2015.426
10.1007/s10994-007-5040-8
10.1007/s10589-016-9832-2
10.1007/s10589-021-00288-1
10.1137/0916069
10.1109/TCBB.2010.22
10.1023/A:1007379606734
10.1214/15-AOS1388
10.1186/1471-2105-11-181
10.1109/TITS.2016.2598356
10.1287/ijoc.2020.1031
10.1109/TPAMI.2015.2452911
10.2307/2348496
10.1109/TBME.2009.2036000
10.21437/Interspeech.2015-265
10.1109/ICASSP.2015.7178814
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key-10.3934/mine.2023020-20
key-10.3934/mine.2023020-42
key-10.3934/mine.2023020-21
key-10.3934/mine.2023020-43
key-10.3934/mine.2023020-26
key-10.3934/mine.2023020-27
key-10.3934/mine.2023020-24
key-10.3934/mine.2023020-25
key-10.3934/mine.2023020-28
key-10.3934/mine.2023020-29
key-10.3934/mine.2023020-40
key-10.3934/mine.2023020-41
key-10.3934/mine.2023020-1
key-10.3934/mine.2023020-2
key-10.3934/mine.2023020-11
key-10.3934/mine.2023020-33
key-10.3934/mine.2023020-3
key-10.3934/mine.2023020-12
key-10.3934/mine.2023020-34
key-10.3934/mine.2023020-4
key-10.3934/mine.2023020-31
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key-10.3934/mine.2023020-15
key-10.3934/mine.2023020-37
key-10.3934/mine.2023020-7
key-10.3934/mine.2023020-16
key-10.3934/mine.2023020-38
key-10.3934/mine.2023020-8
key-10.3934/mine.2023020-13
key-10.3934/mine.2023020-35
key-10.3934/mine.2023020-9
key-10.3934/mine.2023020-14
key-10.3934/mine.2023020-36
key-10.3934/mine.2023020-19
key-10.3934/mine.2023020-17
key-10.3934/mine.2023020-39
key-10.3934/mine.2023020-18
key-10.3934/mine.2023020-30
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– ident: key-10.3934/mine.2023020-21
  doi: 10.1609/aaai.v29i1.9581
– ident: key-10.3934/mine.2023020-41
  doi: 10.1609/aaai.v27i1.8577
– ident: key-10.3934/mine.2023020-5
  doi: 10.1145/1645953.1646169
– ident: key-10.3934/mine.2023020-8
  doi: 10.1214/16-STS602
– ident: key-10.3934/mine.2023020-20
– ident: key-10.3934/mine.2023020-32
  doi: 10.1109/ICCV.2011.6126288
– ident: key-10.3934/mine.2023020-15
  doi: 10.1007/s10589-019-00134-5
– ident: key-10.3934/mine.2023020-24
– ident: key-10.3934/mine.2023020-10
  doi: 10.1561/9781601984616
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– ident: key-10.3934/mine.2023020-30
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– ident: key-10.3934/mine.2023020-38
– ident: key-10.3934/mine.2023020-40
  doi: 10.1145/2538028
– ident: key-10.3934/mine.2023020-2
  doi: 10.1145/2556195.2556264
– ident: key-10.3934/mine.2023020-13
  doi: 10.1145/2020408.2020423
– ident: key-10.3934/mine.2023020-27
  doi: 10.1016/j.ejor.2015.06.081
– ident: key-10.3934/mine.2023020-29
  doi: 10.1109/ICCV.2015.426
– ident: key-10.3934/mine.2023020-4
  doi: 10.1007/s10994-007-5040-8
– ident: key-10.3934/mine.2023020-42
– ident: key-10.3934/mine.2023020-28
  doi: 10.1007/s10589-016-9832-2
– ident: key-10.3934/mine.2023020-14
  doi: 10.1007/s10589-021-00288-1
– ident: key-10.3934/mine.2023020-11
  doi: 10.1137/0916069
– ident: key-10.3934/mine.2023020-37
  doi: 10.1109/TCBB.2010.22
– ident: key-10.3934/mine.2023020-12
  doi: 10.1023/A:1007379606734
– ident: key-10.3934/mine.2023020-9
  doi: 10.1214/15-AOS1388
– ident: key-10.3934/mine.2023020-23
– ident: key-10.3934/mine.2023020-25
  doi: 10.1186/1471-2105-11-181
– ident: key-10.3934/mine.2023020-26
  doi: 10.1109/TITS.2016.2598356
– ident: key-10.3934/mine.2023020-19
  doi: 10.1287/ijoc.2020.1031
– ident: key-10.3934/mine.2023020-43
  doi: 10.1109/TPAMI.2015.2452911
– ident: key-10.3934/mine.2023020-18
  doi: 10.2307/2348496
– ident: key-10.3934/mine.2023020-16
– ident: key-10.3934/mine.2023020-31
  doi: 10.1109/TBME.2009.2036000
– ident: key-10.3934/mine.2023020-33
– ident: key-10.3934/mine.2023020-39
– ident: key-10.3934/mine.2023020-6
– ident: key-10.3934/mine.2023020-22
  doi: 10.21437/Interspeech.2015-265
– ident: key-10.3934/mine.2023020-36
  doi: 10.1109/ICASSP.2015.7178814
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SubjectTerms clustered mtl
global optimization
miqp
multitask learning
weakly constrained mtl
Title Mixed-integer quadratic programming reformulations of multi-task learning models
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