Work out hyperparameter search trials instantly with clear inputs, formula shown and shareable results.
Grid search cost is values raised to the power of parameters, so it explodes past three or four dimensions. Random search escapes that because the probability of missing the top p fraction of configurations in n draws is (1-p)^n: 60 random trials find a top-5-percent configuration with 95 percent probability regardless of dimensionality. Bayesian optimisation improves further by fitting a surrogate, needing roughly ten trials per dimension.
Search budgets
grid = values^parameters; random search: P(hit top p) = 1 - (1-p)^n; Bayesian: roughly 10 trials per hyperparameter
Most hyperparameters barely matter. Grid search wastes trials varying unimportant dimensions at fixed values of important ones, while random search samples every dimension at a distinct value each trial.
With one or two parameters, or when you need an exhaustive, reproducible sweep for a report. Otherwise prefer random or Bayesian search.