Unified Smoothing Approach for Best Hyperparameter Selection Problem Using a Bilevel Optimization Strategy

Strongly motivated from use in various fields including machine learning, the methodology of sparse optimization has been developed intensively so far. Especially, the recent advance of algorithms for solving problems with nonsmooth regularizers is remarkable. However, those algorithms suppose that weight parameters of regularizers, called hyperparameters hereafter, are pre-fixed, and it is a crucial matter how the best hyperparameter should be selected. In this paper, we focus on the hyperparameter selection of regularizers related to the $\ell_p$ function with $0

Keywords:

• Selection (genetic algorithm)
• Mathematical optimization
• Focus (optics)
• Hyperparameter optimization
• Computer science
• Smoothing
• Hyperparameter
• Bilevel optimization
• Function (mathematics)
• Class (set theory)

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