Optimize function with Bayesian Optimization

Hi,

I'm working with a simple example in trying to understand Bayesian Optimization.

Suppose I want to find the minimum of the 2-Dimensional Rastrigin function (this has a global minimum at coordinates (0,0)).

% Rastrigin function
fun = @(x,y)reshape(rastriginsfcn([x(:)/10,y(:)/10]),size(x));
fsurf(fun,[-30 30],'ShowContours','on')
title('rastriginsfcn([x/10,y/10])')
xlabel('x')
ylabel('y')

Now, I want to use Bayesian Optimization in order to minimize this function, but I can't seem to get it to work.w

Here is the code that I use.

% Variables for a Bayesian Optimization
X1 = optimizableVariable('x',[-30 30]);
X2 = optimizableVariable('y',[-30 30]);
vars = [X1,X2];

% Function to Optimize
fun = @(x)rastriginsfcn(x./10);

results = bayesopt(fun,vars,'AcquisitionFunctionName','expected-improvement-plus');

This code just gives me the error "Undefined function 'rdivide' for input arguments of type 'table'.".

Answer 1

[Alan Weiss]

As clearly stated in the documentation for bayesopt, the function passes a TABLE of values. However, rastriginsfcn expects a 2-D double array. You need to write your own objective function for bayesopt, and cannot rely on those provided by Global Optimization Toolbox.

function fval = myrastrig(in)
x(1) = in.x;
x(2) = in.y;
fval = rastriginsfcn(x/10);
end

Then call the function as follows:

results = bayesopt(@myrastrig,vars)

Alan Weiss

MATLAB mathematical toolbox documentation

[Subhodip Biswas]

This example works well for a 2D functin. How can this code be automated if I have functions in 10D, 30D, and so on?

[Alan Weiss]

I think that you would be best served by surrogateopt rather than bayesopt for this case. The solvers have similar underlying mechanisms, but surrogateopt allows you to use higher-dimensional variables easily. bayesopt requires you to create variables one dimension at a time.

That said, is your problem very computationally demanding, with a slow-to-compute objective function? If not, then fmincon or patternsearch are usually better solvers for smooth and nonsmooth problems respecitvely.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation