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In this paper, we propose the use of a black-box optimization method calleddeterministic Mesh Adaptive Direct Search (MADS) algorithm with orthogonaldirections (Ortho-MADS) for the selection of hyperparameters of Support VectorMachines with a Gaussian kernel. Different from most of the methods in theliterature that exploit the properties of the data or attempt to minimize theaccuracy of a validation dataset over the first quadrant of (C, gamma), theOrtho-MADS provides convergence proof. We present the MADS, followed by theOrtho-MADS, the dynamic stopping criterion defined by the MADS mesh size andtwo different search strategies (Nelder-Mead and Variable Neighborhood Search)that contribute to a competitive convergence rate as well as a mechanism toescape from undesired local minima. We have investigated the practicalselection of hyperparameters for the Support Vector Machine with a Gaussiankernel, i.e., properly choose the hyperparameters gamma (bandwidth) and C(trade-off) on several benchmark datasets. The experimental results have shownthat the proposed approach for hyperparameter tuning consistently findscomparable or better solutions, when using a common configuration, than othermethods. We have also evaluated the accuracy and the number of functionevaluations of the Ortho-MADS with the Nelder-Mead search strategy and theVariable Neighborhood Search strategy using the mesh size as a stoppingcriterion, and we have achieved accuracy that no other method forhyperparameters optimization could reach.

A Novel Orthogonal Direction Mesh Adaptive Direct Search Approach for SVM Hyperparameter Tuning