Hyper-parameter optimization for support vector machines using stochastic gradient descent and dual coordinate descent

We developed a gradient-based method to optimize the regularization hyper-parameter, C, for support vector machines in a bilevel optimization framework. On the upper level, we optimized the hyper-parameter C to minimize the prediction loss on validation data using stochastic gradient descent. On the lower level, we used dual coordinate descent to optimize the parameters of support vector machines to minimize the loss on training data. The gradient of the loss function on the upper level with respect to the hyper-parameter, C, was computed using the implicit function theorem combined with the optimality condition of the lower-level problem, i.e., the dual problem of support vector machines. We compared our method with the existing gradient-based method in the literature on several datasets. Numerical results showed that our method converges faster to the optimal solution and achieves better prediction accuracy for large-scale support vector machine problems.