A novel orthogonal direction mesh adaptive direct search approach for svm hyperparameter tuning
A novel orthogonal direction mesh adaptive direct search approach for svm hyperparameter tuning
Mello, Alexandre R. and De Matos, Jonathan and Stemmer, Marcelo R. and De S. Britto, Alceu and Koerich, Alessandro L.
arXiv 2019
Abstract : In this paper, we propose the use of a black-box optimization method called deterministic Mesh Adaptive Direct Search (MADS) algorithm with orthogonal directions (Ortho-MADS) for the selection of hyperparameters of Support Vector Machines with a Gaussian kernel. Different from most of the methods in the literature that exploit the properties of the data or attempt to minimize the accuracy of a validation dataset over the first quadrant of (C, $γ$), the Ortho-MADS provides convergence proof. We present the MADS, followed by the Ortho-MADS, the dynamic stopping criterion defined by the MADS mesh size and two different search strategies (Nelder-Mead and Variable Neighborhood Search) that contribute to a competitive convergence rate as well as a mechanism to escape from undesired local minima. We have investigated the practical selection of hyperparameters for the Support Vector Machine with a Gaussian kernel, i.e., properly choose the hyperparameters $γ$(bandwidth) and C (trade-off) on several benchmark datasets. The experimental results have shown that the proposed approach for hyperparameter tuning consistently finds comparable or better solutions, when using a common configuration, than other methods. We have also evaluated the accuracy and the number of function evaluations of the Ortho-MADS with the Nelder-Mead search strategy and the Variable Neighborhood Search strategy using the mesh size as a stopping criterion, and we have achieved accuracy that no other method for hyperparameters optimization could reach.
