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An efficient primal-dual method for solving non-smooth machine learning problem

Author

Listed:
  • Lyaqini, S.
  • Nachaoui, M.
  • Hadri, A.

Abstract

This paper deals with the machine learning model as a framework of regularized loss minimization problem in order to obtain a generalized model. Recently, some studies have proved the success and the efficiency of nonsmooth loss function for supervised learning problems Lyaqini et al. [1]. Motivated by the success of this choice, in this paper we formulate the supervised learning problem based on L1 fidelity term. To solve this nonsmooth optimization problem we transform it into a mini-max one. Then we propose a Primal-Dual method that handles the mini-max problem. This method leads to an efficient and significantly faster numerical algorithm to solve supervised learning problems in the most general case. To illustrate the effectiveness of the proposed approach we present some experimental-numerical validation examples, which are made through synthetic and real-life data. Thus, we show that our approach is outclassing existing methods in terms of convergence speed, quality, and stability of the predicted models.

Suggested Citation

  • Lyaqini, S. & Nachaoui, M. & Hadri, A., 2022. "An efficient primal-dual method for solving non-smooth machine learning problem," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921011085
    DOI: 10.1016/j.chaos.2021.111754
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    References listed on IDEAS

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    1. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    2. Mee Young Park & Trevor Hastie, 2007. "L1‐regularization path algorithm for generalized linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 659-677, September.
    3. Adi L Tarca & Vincent J Carey & Xue-wen Chen & Roberto Romero & Sorin Drăghici, 2007. "Machine Learning and Its Applications to Biology," PLOS Computational Biology, Public Library of Science, vol. 3(6), pages 1-11, June.
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