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Enhancing deep learning algorithm accuracy and stability using multicriteria optimization: an application to distributed learning with MNIST digits

Author

Listed:
  • Davide La Torre

    (Université Côte d’Azur)

  • Danilo Liuzzi

    (University of Milan)

  • Marco Repetto

    (Université Côte d’Azur
    University of Milan-Bicocca
    Siemens Italy)

  • Matteo Rocca

    (Universitá degli Studi dell’Insubria)

Abstract

The training phase is the most crucial stage during the machine learning process. In the case of labeled data and supervised learning, machine learning entails minimizing the loss function under various constraints. We provide an innovative model for learning with numerous data sets, resulting from the application of multicriteria optimization techniques to existing deep learning algorithms. Data fitting is formulated as a multicriteria model in which each criterion measures the data fitting error on a specific data set. This is an optimization model involving a vector-valued function, and it has to be analyzed using the notion of Pareto efficiency. We present stability results for efficient solutions in the presence of input and output data perturbations. The multiple data set environment comes into play to eliminate the bias caused by the selection of a specific training set. To apply this concept, we present a scalarization strategy as well as numerical experiments in digit classification using MNIST data.

Suggested Citation

  • Davide La Torre & Danilo Liuzzi & Marco Repetto & Matteo Rocca, 2024. "Enhancing deep learning algorithm accuracy and stability using multicriteria optimization: an application to distributed learning with MNIST digits," Annals of Operations Research, Springer, vol. 339(1), pages 455-475, August.
    • Handle: RePEc:spr:annopr:v:339:y:2024:i:1:d:10.1007_s10479-022-04833-x
    DOI: 10.1007/s10479-022-04833-x
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    References listed on IDEAS

    as
    1. Herb Kunze & Davide Torre, 2022. "Solving inverse problems for steady-state equations using a multiple criteria model with collage distance, entropy, and sparsity," Annals of Operations Research, Springer, vol. 311(2), pages 1051-1065, April.
    2. Faizal Hafiz & Jan Broekaert & Davide La Torre & Akshya Swain, 2021. "A Multi-criteria Approach to Evolve Sparse Neural Architectures for Stock Market Forecasting," Papers 2111.08060, arXiv.org.
    3. Saeed Nosratabadi & Sina Ardabili & Zoltan Lakner & Csaba Mako & Amir Mosavi, 2021. "Prediction of Food Production Using Machine Learning Algorithms of Multilayer Perceptron and ANFIS," Papers 2104.14286, arXiv.org.
    Full references (including those not matched with items on IDEAS)

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