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So when you search randomly and reach up to a set of optimised parameters, how do you know if it can't be optimised any further, since you haven't looked up all possible sets like in a grid?

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You generally don't know if you've reached a suitable maxima, which is why it is good to run a nondeterministic optimizer a few times (if computation power allows) and see if there are any reliable parameters form there.

There are also somewhat better-than-random strategies such as Bayesian optimization and particle swarm optimization that can help you to search more efficiently.

Grid search never exhausts the search space either, at least if the dimensions are continuous.

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