Bayesian Optimization: Probability of Improvement
Advanced
The problem, from first principles
Probability of improvement is the simplest Bayesian optimization rule. It scores a candidate by the chance that its true value lands below the best so far. It ignores how much the improvement would be, which is the weakness expected improvement fixes.
From theory to code
Implement probability_of_improvement(mu, sigma, best) for minimization, returning the standard normal CDF of (best - mu) / sigma.
Constraints
sigmais positive.
Hints
Hint 1
Compute z = (best - mu) / sigma and return Phi(z) using math.erf.
Keywords
research-papersclassical-mlbayesian-optimizationhyperparameters
Python
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