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Gaussian Process
A non-parametric probabilistic model that defines a distribution over functions, characterized by a mean function and a covariance function (kernel).
Acquisition Function
A heuristic function that guides the selection of the next evaluation point by balancing exploration and exploitation based on the surrogate model.
Expected Improvement (EI)
An acquisition function that calculates the expected improvement over the current best observation, weighted by its probability of occurrence.
Probability of Improvement (PI)
An acquisition function that maximizes the probability of improvement over the current best point, without considering the magnitude of the improvement.
Kernel Function
A function that measures the similarity between input points and defines the covariance structure of the Gaussian process, influencing the smoothness of the modeled function.
Hyperprior
A prior distribution on the model's hyperparameters (such as kernel parameters), allowing for the automatic learning of these parameters through Bayesian inference.
Sequential Model-Based Optimization (SMBO)
A general optimization framework that uses a sequential model to propose new evaluation points based on previous observations.
Multi-Objective Bayesian Optimization
An extension of Bayesian Optimization to handle multiple conflicting objectives, searching for the optimal Pareto front rather than a single optimum.
Noise Handling
Techniques for modeling and managing noise in objective function observations, essential for real-world applications with noisy evaluations.
Parallel Bayesian Optimization
Variant that proposes several points simultaneously for parallel evaluation, using acquisition criteria adapted for batch selection.
Kernel Design
Process of designing or selecting the appropriate covariance function to capture the specific properties of the objective function.
Acquisition Optimization
Secondary optimization problem consisting of maximizing the acquisition function to find the next candidate evaluation point.