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Probability of Improvement (PI)
Acquisition function that selects the point with the highest probability of exceeding a certain improvement threshold, primarily favoring the exploitation of known areas.
Hyperparameter of noise
Parameter of the Gaussian process that models the variance of noise in the objective function observations, essential for handling noisy data.
Kernel
Function defining the covariance between two points in a Gaussian process, determining the regularity and properties of the modeled function (e.g., RBF kernel, Matérn).
Regret
Performance measure in Bayesian optimization, quantifying the difference between the value of the global optimum and the best value found so far.
Maximization of the Expected A Posteriori (MAP)
Phase of Bayesian optimization where the point that maximizes the acquisition function is found, often performed using multi-start optimization methods or grid search.
Mutual Information Entropy
Advanced acquisition function that selects the point maximizing the expected reduction in entropy regarding the location of the global optimum, favoring highly targeted exploration.
GP-UCB
Variant of the upper confidence bound specifically derived for Gaussian processes, with theoretical guarantees on cumulative regret.
Multi-objective Bayesian Optimization
Extension of Bayesian optimization to problems with multiple conflicting objectives, using adapted acquisition functions such as Expected Hypervolume Improvement.