Purely Explorative Acquisition Functions for bayesopt

Hello, I am trying to use Bayesian Optimization with the goal of learning the surrogate function as accurately as possible instead of its maximization. Essentially, I would like to use bayesopt, but with a purely explorative aquisition function like LCB with a high exploration constant (or without the mean entirely) or the Integrated Variance Reduction function described (not originally) here.

Is there any way to do this? I don't see any documented way to modify the LCB function or use a custom aquisition function.

Answer 1

[Parag]

Hi, you want to use ‘bayesopt’ with a purely explorative aquisition function but as per documentation of ‘bayesopt’. You can take a look at documenation for more detail.

https://www.mathworks.com/help/stats/bayesopt.html

Even as per a previous question answered by MathWorks staff there is no way to use your own custom acquisition function in ‘bayesopt’

You can check the previous question answered by staff-

https://www.mathworks.com/matlabcentral/answers/391772-how-to-implement-a-custom-acquisition-function-for-the-bayesopt-package-in-matlab#answer_313103

% Define your objective function (e.g., a simple quadratic function)
objectiveFunction = @(x) (x - 0.3).^2 + sin(5*x);

% Initial sample points
xInitial = linspace(0, 1, 5)'; % Initial points (column vector)
yInitial = objectiveFunction(xInitial); % Evaluate the objective function

% Fit initial Gaussian Process model
gprMdl = fitrgp(xInitial, yInitial, 'BasisFunction', 'constant', 'KernelFunction', 'squaredexponential', 'Sigma', 0.1);

% Number of iterations for Bayesian Optimization
numIterations = 20;
kappa = 2.0; % Exploration parameter for LCB

% Explore the function space
for iter = 1:numIterations
    % Define a fine grid over the input space
    xGrid = linspace(0, 1, 1000)';

    % Predict using the GP model
    [predY, predSD] = predict(gprMdl, xGrid);

    % Calculate LCB
    lcbValues = predY - kappa * predSD;

    % Choose the next point based on minimum LCB value
    [~, nextIdx] = min(lcbValues);
    nextPoint = xGrid(nextIdx);

    % Evaluate the objective function at the new point
    newY = objectiveFunction(nextPoint);

    % Update the dataset
    xInitial = [xInitial; nextPoint];
    yInitial = [yInitial; newY];

    % Refit the Gaussian Process model
    gprMdl = fitrgp(xInitial, yInitial, 'BasisFunction', 'constant', 'KernelFunction', 'squaredexponential', 'Sigma', 0.1);

    % Plot the current state
    figure(1);
    clf;
    hold on;
    plot(xGrid, objectiveFunction(xGrid), 'r--', 'LineWidth', 1.5); % True function
    plot(xInitial, yInitial, 'bo', 'MarkerSize', 6, 'MarkerFaceColor', 'b'); % Sampled points
    plot(xGrid, predY, 'b-', 'LineWidth', 1.5); % Predicted mean
    fill([xGrid; flipud(xGrid)], [predY + 2*predSD; flipud(predY - 2*predSD)], 'b', 'FaceAlpha', 0.1, 'EdgeColor', 'none'); % Confidence interval
    plot(xGrid, lcbValues, 'g-', 'LineWidth', 1.5); % LCB values
    title(sprintf('Iteration %d', iter));
    xlabel('x');
    ylabel('f(x)');
    legend('True Function', 'Sampled Points', 'GP Prediction', 'Confidence Interval', 'LCB');
    hold off;
    pause(0.5); % Pause to visualize the updates
end

% Display final sampled points and function evaluations
disp('Final Sampled Points:');

disp(xInitial);
disp('Function Evaluations:');
disp(yInitial);

You can see the documentation for ‘fitrgp’ for more detail-

https://www.mathworks.com/help/stats/fitrgp.html