Glosarium AI
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Constrained Bayesian Optimization
Extension of Bayesian optimization that incorporates constraints on input or output variables, guiding the search for the optimum only within the feasible subspace defined by these constraints.
Constrained Acquisition Function
Modified acquisition function that penalizes points violating constraints, combining exploration and exploitation with a feasibility probability to evaluate the utility of a candidate point.
Feasibility Probability Model
Stochastic model, often a Gaussian process, that estimates the probability that a given point satisfies all constraints of the optimization problem.
Gaussian Process Classification
Use of a Gaussian process to model the binary output of a constraint (satisfied or violated), allowing estimation of feasibility probability across the entire search space.
Expected Constrained Improvement (ECI)
Acquisition function that calculates the expected improvement on the objective function, weighted by the probability that the candidate point satisfies the constraints.
Constrained Upper Confidence Bound (C-UCB)
Variant of the UCB acquisition function that incorporates a confidence term on feasibility, favoring points that are both promising for the objective and likely to be feasible.
Constrained Knowledge Gradient
Acquisition strategy that evaluates the expected future value of information by considering the impact of evaluations on knowledge of the feasibility boundary and the optimum.
Constraint Set
Collection of constraints (inequalities or equalities) that candidate solutions must satisfy, modeled individually or in an aggregated manner within the Bayesian optimization framework.
Feasibility Boundary
Surface or hypersurface in the search space that separates feasible regions (satisfying constraints) from infeasible regions, whose discovery is a major challenge.
Constraint Violation
Quantitative measure of the non-compliance with a constraint by a given point, often used to penalize infeasible solutions in the acquisition function.
Constrained Black-Box Optimizer
Optimization algorithm designed for black-box functions where evaluations are expensive and subject to constraints, typically implemented via Bayesian optimization.
Constrained Rejection Sampling
Initialization or exploration method where points are generated and then rejected if they do not meet a set of preliminary feasibility criteria.
Constrained Surrogate Model
Model (e.g., Gaussian process) that learns both the objective function and constraint functions, allowing prediction of performance and feasibility at any unevaluated point.
Adaptive Sampling Strategy
Approach where the sampling policy dynamically evolves to balance learning of the objective function and feasibility boundary based on gathered information.
Integrated Penalty
Technique transforming a constrained problem into an unconstrained one by adding a penalty to the objective function, proportional to the magnitude of constraint violation.
Feasible Search Space
Subset of the original search space defined by the set of constraints, within which the algorithm is allowed to search for the optimum.
Multi-Objective Constrained Sequential Acquisition
Extension of Bayesian optimization to problems with multiple conflicting objectives and constraints, where the acquisition function manages a feasible Pareto front.