Title: Assessing DCA Convergence in Minimizing Gaussian RBF Support Vector Regression Prediction Functions

Original: arXiv:2606.03559v1 Announce Type: new Abstract: This study introduces a framework for tackling nonconvex optimization problems where the objective is the prediction function derived from a Support Vector Regression (SVR) model trained with a Gaussian radial basis function (RBF) kernel (RBF-SVR). The approach leverages the Difference of Convex functions (DC) algorithm (DCA), utilizing the analytical properties of the RBF kernel to establish an explicit DC decomposition. We successfully derive closed-form expressions for the lower bound $\mu$, representing the strong convexity parameter of the DC components, and the upper bound $L$, corresponding to the gradient Lipschitz constant of the subproblem. These parameters, $\mu$ and $L$, are exclusively defined by the post-training sum of dual coefficients ($C_{\alpha}$), the RBF kernel parameter $\gamma$, and the DC decomposition parameter $\rho$. Notably, they share a dominant leading term, $C_{\alpha}\rho$. Our numerical experiments, conducted across six benchmark functions, reveal that $C_{\alpha}\rho$ serves as the key single metric defining both the convergence behavior and the sensitivity to initial points for DCA. Furthermore, we illustrate that this quantity splits into two distinct, independent pathways: $C \to C_{\alpha}$ and $\gamma \to \rho$, with its main fluctuations driven by the SVR hyperparameters $(C, \gamma)$. Collectively, these findings enable the pre-assessment of DCA’s convergence characteristics on RBF-SVR via the scalar $C_{\alpha}\rho$. This assessment can be approximated using $(C, \gamma)$ prior to training or calculated exactly in closed form following training.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC