# 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?

• stats.stackexchange.com/questions/84012/… seems very related Jun 25 '14 at 10:46
• You're asking about a grid search with non-uniform steps. I've never seen it done (for alpha) but if you want to investigate it, then go ahead. I'm skeptical it will give improvement. Please post some numbers if you find otherwise.
– smci
Jul 6 '15 at 21:51
• I remember a nice trick from Andrew Ng's lectures: 1, 0.3, 0.1, 0.03, 0.01, 0.003, 0.001. It's approximately logarithmic but looks neat. If you don't care about your grid looking neat, just choose any logarithmic grid, i.e. start with 1 and divide by two: 1, 0.5, 0.25, 0.125, 0.0625..., or by five, or by ten. Jul 6 '15 at 22:46