Sorry for the double post - I accidentially hit my the "send" button...
We want to build a global optimizer for extremely expensive noisy objective
functions based
on physical measurements.
Our approach is based on optimizing kriging response surfaces surface models.
(as seen in www.cs.ubc.ca/~hutter/earg/stack/taxonomy-global_optimization.pdf)
In each iteration, we
- model the response surface based on the measurements done so far
using "Krig"
from "fields".
- find a parameter set that maximizes the probability of improvement on
this model
using "constrOptim" from multiple starting points.
- measure the parameter set that maximizes the probability of
improvement
My problem:
Unfortunately, the optimizations are extremely slow (~30s per iteration of the
algorithm)
despite not making excessive numbers of objective function evaluations (~1000
per
iteration).
I suspect this is because the many calls of predict.Krig and predict.se.Krig
made by "optim"
are slow, compared to a single call with many x values:
##example code:
library(fields)
fun<-function(x){return(sin(x*9)*1/((x)^2+0.02))}
#make some kriging model of a nasty objective function
x=matrix(seq(-1,1,0.5),ncol=1)
y=apply(x,2,fun)
kfit=Krig(x,y,cov.function=Exp.cov,p=2,theta=0.2)
#this is fast:
xp=matrix(seq(-1,1,0.001),ncol=1)
yp=predict.se(kfit,xp)
#this is _very_ slow:
for(i in 1:nrow(xp)){
yp[i]=predict.se(kfit,xp[i,])
}
##end example code
My question:
how can I speed up the many single predictions so they can be used efficiently
in an
objective-function in an optimization?
thanks!
Felix Bonowski
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