At which epochs does the hyperband algorithm of wandb checks for improvement?

Question

I am trying to use hyperparameter-tuning(aka sweep) feature of the wandb library (link to its official page). And I am trying to apply bayesian hyperband algorithm.

Now as mentioned in these pages (how sweep config is defined), (what are the parameters related to the early terminate option), under early terminate we have to mention 4 params (generally), those are min_iter, s, eta and max_iter, it would look something like follows.

My doubts summarized:

In summary, what I want to know, Given all 4 :- min_iter, s, eta, and max_iter

1. at which epochs will the hyperband algorithm check for improvement??

2. considering I am trying to do bayesian hyperband, how many runs will be evaluated in the first bracket, and how many runs will be evaluated in the consecutive brackets?

3. is there any way or rule(s) of thumb to decide what values are good to take for these 4 parameters(min_iter, s, eta, and max_iter) ?

4. please explain about the paramters s and eta (especially eta) in a bit more detail, i.e. with a bit or underlying maths (please keep it simple if possible).

What is my doubt about? (explained in a bit more detail/context):

(Here), they have somewhat explained that at which epochs (their) implementation of the hyperband algorithm checks for improvement and takes decision whether to terminate a run or not.

When only the minimum number of iterations for each run are our concern

When only the minimum number of iterations for each run are our concern

But what about a case when both the minimum and maximum number of iterations for each run are our concern?? Like the one as follows...

#in a yaml file to be used by wanbd in python
early_terminate:
  type: hyperband
  min_iter: 10
  s: 3
  eta: 4
  max_iter: 50

What I have already tried:

I have even tried my best to read the original paper and try to understand what's going on (or what might be going on) (link to the original paper on the hyperband algorithm), but wasn't able to get satisfactory answers.

I have even tried to visit their github pages where there are examples, but they have only shown how to write a config, not explained that what it does in depth.