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Is there a way to combine both grid search and random search together ?

Lets say I provided a very big range of hyper parameters, can I use random search to minimize this range, and then I follow it back with grid search over this minimized range ? If yes what is the exact methodology to do so ?

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One simple way to do it is taking random samples across the space and creating additional grids at a finer resolution where your performance is good. Another way is to use Bayesian HPO all the way, which in a way does it for you. For python it's available in scikit-optimize package.

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