Expected Improvement

Expected Improvement (EI) is an acquisition function that scores candidates based on the expected improvement over the current best observation. It balances exploitation (selecting candidates with high predicted values) and exploration (selecting candidates with high uncertainty).

class alf_tools.optimizer.acquisition_functions.expected_improvement.ExpectedImprovement

Bases: AcquisitionFunction

Expected improvement acquisition function.

The Expected Improvement acquisition value is given by: EI = (μ - best_f) * Φ(z) + σ * φ(z), where μ is the mean prediction, σ is the standard deviation, best_f is the best observed value, z is (μ - best_f) / σ, and Φ and φ are the CDF and PDF of the standard normal distribution. Higher EI values indicate more improvement over the best observed value. This is a maximising acquisition function.