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What is the correct strategy of using Grid Search? Am I understand correctly that to use correctly Grid Search I should:

  1. Give Grid Search initial parameters that have wide range. For example if parameter alpha usually ranges from 0 to 100 I should give list of parameters like [0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100] and if parameter beta usually ranges from 0.1 to 0.0001 give list of parameters [0.1, 0.01, 0.001, 0.0001]?

  2. Now we picked the parameters 'alpha': [0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100], 'beta':[0.1, 0.01, 0.001, 0.0001] and we run Grid Search with them.

  3. We got best parameters from Grid Search: 'alpha': 50, 'beta':0.0001

What is the next step here? How should we run Grid Search again with:

Variant 1:

'alpha': [0, 10, 20, 30, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 70, 80, 90, 100], 'beta':[0.1, 0.01, 0.001, 0.0001, 0.00001, 0000001]

OR

Variant 2

 'alpha': [42, 44, 46, 48, 50, 52, 54, 56, 58], 'beta':[0.0001, 0.00001, 0000001]

Is variant 2 good variant? I thought that variant 1 is better because the best combination of parameters may be 'alpha': 30, 'beta':0.00001. Is it possible? Or I should remove all parameters that does not perform well in first Grid Search as in variant 2?

  1. Repeat step 3 until found parameters that are giving best score.

So my question is:

  1. Is choosing parameters in step 1 correct way of doing that?
  2. Which variant of step 3 should I use?
  3. How does that strategy looks overall? Is it good strategy or anything should be changed?
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