Log Scale for Hyperparamers Explanaion

[Breno]

In the video “Using an Appropriate Scale to pick Hyperparameters”, it says that if we are tuning the learning rate in the range (0.001, 1) in the iinear scale, 90% of the samples would be in (0.1, 1). I could’t get the mathematical justification for that.

[anon57530071]

Here is an illustration of what Andrew talked.

I think we do not need math, but it is quite simple.

P = \frac{(1-0.1)}{(1-0.0001)} = 0.9001