Post-Pareto Analysis and a New Algorithm for the Optimal Parameter Tuning of the Elastic Net

Henri Bonnel () and Christopher Schneider ()
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Henri Bonnel: Université de la Nouvelle-Calédonie
Christopher Schneider: Ernst-Abbe-Hochschule Jena

Journal of Optimization Theory and Applications, 2019, vol. 183, issue 3, No 11, 993-1027

Abstract: Abstract The paper deals with the optimal parameter tuning for the elastic net problem. This process is formulated as an optimization problem over a Pareto set. The Pareto set is associated with a convex multi-objective optimization problem, and, based on the scalarization theorem, we give a parametrical representation of it. Thus, the problem becomes a bilevel optimization with a unique response of the follower (strong Stackelberg game). Then, we apply this strategy to the parameter tuning for the elastic net problem. We propose a new algorithm called Ensalg to compute the optimal regularization path of the elastic net w.r.t. the sparsity-inducing term in the objective. In contrast to existing algorithms, our method can also deal with the so-called “many-at-a-time” case, where more than one variable becomes zero at the same time and/or changes from zero. In examples involving real-world data, we demonstrate the effectiveness of the algorithm.

Keywords: Post-Pareto analysis; Multi-objective optimization; Bilevel optimization; Linear regression; Sparsity; Elastic net; Linear complementarity problem; 90C29; 65K05; 90C90; 62J05; 90C33 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-019-01592-x

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