Gradient-Free Optimization for GLMNET Parameters

In the post https://statcompute.wordpress.com/2017/09/03/variable-selection-with-elastic-net, it was shown how to optimize hyper-parameters, namely alpha and gamma, of the glmnet by using the built-in cv.glmnet() function. However, following a similar logic of hyper-parameter optimization shown in the post https://statcompute.wordpress.com/2019/02/10/direct-optimization-of-hyper-parameter, we can directly optimize alpha and gamma parameters of the glmnet by using gradient-free optimizations, such as Nelder–Mead simplex or particle swarm. Different from traditional gradient-based optimizations, gradient-free optimizations are often able to find close-to-optimal solutions that are considered “good enough” from an empirical standpoint in many cases that can’t be solved by gradient-based approaches due to noisy and discontinuous functions.

It is very straight-forward to set up the optimization work-flow. All we need to do is writing an objective function, e.g. to maximize the AUC statistic in this specific case, and then maximizing this objective function by calling the optimizer. In the demonstration below, Nelder–Mead simplex and particle swarm optimizers are employed to maximize the AUC statistic defined in the glmnet.optim() function based on a 10-fold cross validation. As shown in the result, both approaches gave very similar outcomes. For whoever interested, please feel free to compare the demonstrated method with the cv.glmnet() function.