Work out random search budget instantly with clear inputs, formula shown and shareable results.
Each random draw has probability p of landing in the top p fraction of configurations, so the chance of missing it n times is (1-p)^n. Solving for the trial count gives n = ln(1 - confidence) / ln(1 - p), which famously yields about 60 trials for a top-5-percent configuration at 95 percent confidence — and crucially that number does not depend on how many hyperparameters there are.
Random search budget
n = ln(1 - confidence) / ln(1 - p); expected best percentile ~ 100 / (n + 1)
Because the target is defined as a fraction of the space, not a specific point. Adding dimensions makes the space larger but the top 5 percent is still 5 percent of draws.
Sample learning rates and regularisation strengths log-uniformly. Linear sampling of a range spanning several orders of magnitude wastes almost every draw on the largest decade.