Should I use grid search with non-uniform steps to determine good $\alpha$ for elastic net? Using the paramater names from What is lambda in an elastic net model (penalized regression)? I wonder about best practices or suggestions for how to determine $\alpha$, i.e. the paramater determining the weighting of the Lasso and the Ridge.
My guess is that one does a 1 dimensional grid search (is there another term for that btw?) starting with 0.5 and then going of towards 0 and 1. My feeling here is that we want to not go off with the same step size all the time. I mean if one of these values is much bigger than the other perhaps we want a value really close to 0 or 1 to compensate? But how close to 0 and 1 do we test? What is the standard approach here? Is there such a thing?
 A: Grid search using cross-validation is the standard approach. Like with any hyper-parameters/penalty optimization, getting a "good" grid involves much trial and error. But typically, model performance will be reasonably smooth in the parameters (i.e., you don't get wild fluctuations in cross-validated error by changing the penalties a little bit), so you can choose as big a grid as you have computing power / patience / coffee for (say 10-50 values), and that is typically enough in what I've seen.
If that's not enough, you can plot it and then focus on regions that need more exploring. Also, in a lot of real data too much tuning has not much effect on performance in external validation on other datasets, so you might not need to do that much to get the optimal performance in external validation.
The one thing to be careful with is that with alpha close to zero you will get closer to ridge regression which can be very slow if you have a lot of predictors (at least if using glmnet or similar methods), as all of them will be in the model making some of the computational shortcuts moot (active-set convergence etc).
