Analytical Evaluation of DCA Convergence Properties for Minimizing Prediction Functions of Gaussian RBF Support Vector Regression

arXiv:2606.03559v1 Announce Type: new Abstract: For nonconvex optimization problems whose objective is the prediction function of a trained Support Vector Regression (SVR) model with the Gaussian radial basis function (RBF) kernel (RBF-SVR), we present a framework that applies the difference of convex functions (DC) algorithm (DCA) by exploiting the analytical structure of the RBF kernel to construct an explicit DC decomposition. Specifically, we derive in closed form both the lower bound mu of the strong convexity parameter of the DC components and the upper bound L of the gradient Lipschitz constant of the subproblem. Both mu and L are determined solely by the post-training dual-coefficient sum C_{alpha} and the RBF kernel parameter gamma, together with the DC decomposition parameter rho, and they share a common leading term C_{alpha}rho. Through numerical experiments on six benchmark functions, we show that C_{alpha}rho is the primary single quantity characterizing both the convergence properties and the initial-point dependence of DCA, and further demonstrate that it decomposes into two independent pathways, C o C_{alpha} and gamma o rho, with its primary variation governed by the SVR hyperparameters (C, gamma). Together, these results allow the convergence properties of DCA on RBF-SVR to be assessed in advance through the single scalar quantity C_{alpha}rho: approximately from (C, gamma) before training, and exactly in closed form after training.

Source: arXiv cs.LG | 2026-06-03