predictError
Predict error value at a set of points
Description
Examples
Error Prediction
This example shows optimizing a function that throws an error when the evaluation point has norm larger than 2. The error model for the objective function learns this behavior.
Create variables named x1 and x2 that range from -5 to 5.
var1 = optimizableVariable('x1',[-5,5]); var2 = optimizableVariable('x2',[-5,5]); vars = [var1,var2];
The following objective function throws an error when the norm of x = [x1,x2] exceeds 2:
function f = makeanerror(x)
f = x.x1 - x.x2 - sqrt(4-x.x1^2-x.x2^2);
fun = @makeanerror;
Plot the error model and minimum objective as the optimization proceeds. Optimize for 60 iterations so the error model becomes well-trained. For reproducibility, set the random seed and use the 'expected-improvement-plus' acquisition function.
rng default results = bayesopt(fun,vars,'Verbose',0,'MaxObjectiveEvaluations',60,... 'AcquisitionFunctionName','expected-improvement-plus',... 'PlotFcn',{@plotMinObjective,@plotConstraintModels});
Predict the error at points on the line x1 = x2. If the error model were perfect, it would have value -1 at every point where the norm of x is no more than 2, and value 1 at all other points.
x1 = (-5:0.5:5)'; x2 = x1; XTable = table(x1,x2); error = predictError(results,XTable); normx = sqrt(x1.^2 + x2.^2); [XTable,table(normx,error)]
ans =
21x4 table
x1 x2 normx error
____ ____ _______ _________
-5 -5 7.0711 0.94663
-4.5 -4.5 6.364 0.97396
-4 -4 5.6569 0.99125
-3.5 -3.5 4.9497 1.0033
-3 -3 4.2426 1.0018
-2.5 -2.5 3.5355 0.99627
-2 -2 2.8284 1.0043
-1.5 -1.5 2.1213 0.89886
-1 -1 1.4142 0.4746
-0.5 -0.5 0.70711 0.0042389
0 0 0 -0.16004
0.5 0.5 0.70711 -0.012397
1 1 1.4142 0.30187
1.5 1.5 2.1213 0.88588
2 2 2.8284 1.0872
2.5 2.5 3.5355 0.997
3 3 4.2426 0.99861
3.5 3.5 4.9497 0.98894
4 4 5.6569 0.98941
4.5 4.5 6.364 0.98956
5 5 7.0711 0.95549