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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Bibliographic Details
Published in:Mathematics in engineering Vol. 5; no. 1; pp. 1 - 16
Main Authors: Lapucci, Matteo, Pucci, Davide
Format: Journal Article
Language:English
Published: AIMS Press 01.03.2023
Subjects:
clustered mtl
global optimization
miqp
multitask learning
weakly constrained mtl
ISSN:2640-3501, 2640-3501
Online Access:Get full text
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Summary: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.
ISSN:2640-3501
2640-3501
DOI:10.3934/mine.2023020