Online Hyperparameter Search Interleaved with Proximal Parameter Updates

• URL: http://arxiv.org/abs/2004.02769v1
• Date: Mon, 6 Apr 2020 15:54:03 GMT
• Title: Online Hyperparameter Search Interleaved with Proximal Parameter Updates
• Authors: Luis Miguel Lopez-Ramos, Baltasar Beferull-Lozano
• Abstract summary: We develop a method that relies on the structure of proximal gradient methods and does not require a smooth cost function. Such a method is applied to Leave-one-out (LOO)-validated Lasso and Group Lasso. Numerical experiments corroborate the convergence of the proposed method to a local optimum of the LOO validation error curve.
• Score: 9.543667840503739
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: There is a clear need for efficient algorithms to tune hyperparameters for statistical learning schemes, since the commonly applied search methods (such as grid search with N-fold cross-validation) are inefficient and/or approximate. Previously existing algorithms that efficiently search for hyperparameters relying on the smoothness of the cost function cannot be applied in problems such as Lasso regression. In this contribution, we develop a hyperparameter optimization method that relies on the structure of proximal gradient methods and does not require a smooth cost function. Such a method is applied to Leave-one-out (LOO)-validated Lasso and Group Lasso to yield efficient, data-driven, hyperparameter optimization algorithms. Numerical experiments corroborate the convergence of the proposed method to a local optimum of the LOO validation error curve, and the efficiency of its approximations.

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