Bayesian Optimization

References

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My understanding of Bayesian optimization is also limited, mainly referencing the following content👇

• 【Machine Learning】Understanding Bayesian Optimization in One Article

• A Detailed Explanation of Bayesian Optimization Principles

• Bayesian Optimization

• Hyperparameter Optimization—Bayesian Optimization and Its Improvement (PBT Optimization)

• Bayesian Optimization

• MATLAB Official Documentation

• Exploring Bayesian Optimization

Advantages and Algorithm Principles

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This section focuses on the advantages of Bayesian optimization and its algorithmic principles. If you are only interested in “how to use it,” you can first learn about the advantages of Bayesian optimization and then skip to MATLAB Usage.

Advantages

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Algorithm Principles

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MATLAB Usage

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Code Overview

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% Define the objective function  
function y = objectiveFcn(x)  
    y = (1 - x.x1)^2 + 100 * (x.x2 - x.x1^2)^2;  
end  

% Define optimization variables  
vars = [optimizableVariable('x1', [-2, 2])  
        optimizableVariable('x2', [-2, 2])];  

% Perform Bayesian optimization  
results = bayesopt(@objectiveFcn, vars, ...  
                   'AcquisitionFunctionName', 'expected-improvement-plus', ...  
                   'MaxObjectiveEvaluations', 30, ...  
                   'IsObjectiveDeterministic', true, ...  
                   'Verbose', 1);  

% View results  
bestPoint = results.XAtMinObjective;  
bestObjective = results.MinObjective;  

fprintf('Optimal solution x1: %.4f, x2: %.4f\n', bestPoint.x1, bestPoint.x2);  
fprintf('Optimal objective value: %.4f\n', bestObjective);  

Parameter Explanation

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For specific options for each parameter, refer to the official documentation: bayesopt. The official documentation is very detailed and includes many examples.