Apply random sampling across the parameter domain to achieve broad coverage with moderate compute is correct.

Apply random sampling across the parameter domain to achieve broad coverage with moderate compute provides broad coverage of the hyperparameter space while letting you limit the total number of trials to fit your compute budget. Random sampling is simple to implement and it tends to find good configurations faster than exhaustive strategies when the space is high dimensional because it does not waste trials on regular intervals. It also avoids the modeling overhead of adaptive methods when you need straightforward, budget conscious exploration.

Use Bayesian optimization to model the performance surface and iteratively propose promising configurations is not chosen here because Bayesian optimization introduces extra complexity and overhead to build a surrogate model and it works best when evaluations are very expensive and you can run many sequential iterations. If you have a tight budget and you want broad coverage quickly then Bayesian methods may not be the most practical choice.

Narrow the parameter ranges and tune only a couple of variables to speed up experiments is not ideal because it risks missing important regions of the search space and it can overlook interactions between parameters. Reducing ranges and dimensions can be useful as a follow up strategy after an initial broad search but it does not by itself provide the broad coverage that the correct option gives.

Run an exhaustive grid search over all parameter combinations regardless of compute constraints is not appropriate because grid search scales exponentially with the number of parameters and quickly becomes infeasible on limited compute. An exhaustive grid may guarantee coverage of a fixed grid but it is very inefficient for high dimensional problems and for large ranges.

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