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Bayesian Optimization Objective Functions

Objective Function Syntax

bayesoptattempts to minimize an objective function. If, instead, you want to maximize a function, set the objective function to the negative of the function you want to maximize. SeeMaximizing Functions。To include extra parameters in an objective function, seeParameterizing Functions。

bayesoptpasses a table of variables to the objective function. The variables have the names and types that you declare; seeVariables for a Bayesian Optimization。

The objective function has the following signature:

[objective,coupledconstraints,userdata] = fun(x)

  1. objective— The objective function value atx, a numeric scalar.bayesoptreturns an error if the objective function returns a nonnumeric value or a matrix with more than one entry.

  2. coupledconstraints— Value of coupled constraints, if any (optional output), a vector of real values. A negative value indicates that a constraint is satisfied, a positive value indicates that it is not satisfied. For details, seeCoupled Constraints。

  3. userdata— Optional data that your function can return for further uses, such as plotting or logging (optional output). For an example, seeBayesian Optimization Plot Functions。

Objective Function Example

This objective function returns the loss in a cross-validated fit of an SVM model with parametersboxandsigma。我们的目标也returns a coupled constraint function that is positive (infeasible) when the number of support vectors exceeds 100 (100 is feasible, 101 is not).

function[objective,constraint] = mysvmfun(x,cdata,grp) SVMModel = fitcsvm(cdata,grp,'KernelFunction','rbf',。..'BoxConstraint',x.box,。..'KernelScale',x.sigma); objective = kfoldLoss(crossval(SVMModel)); constraint = sum(SVMModel.SupportVectors) - 100.5;

To use the objective function, assuming thatcdataandgrpexist in the workspace, create an anonymous function that incorporates the data, as described inParameterizing Functions。

fun = @(x)mysvmfun(x,cdata,grp); results = bayesopt(fun,vars)% Assumes vars exists

Objective Function Errors

bayesoptdeems your objective function to return an error when the objective function returns anything other than a finite real scalar. For example, if your objective function returns a complex value,NaN, orInf, thenbayesoptdeems that your objective function errors. Ifbayesoptencounters an error, it continues to optimize, and automatically updates a Bayesian model of points that lead to errors. This Bayesian model is theError model。bayesoptincorporates the Error model as a coupled constraint. SeeCoupled Constraints。

When errors exist, you can plot the Error model by setting thebayesoptPlotFcnname-value argument@plotConstraintModels。Or you can retrospectively callploton the results of a Bayesian optimization, and include@plotConstraintModels。

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