Not really. In this particular case, I’m minimizing how long it takes a simulation reach one state, so the distribution ends up looking lognormal- or Poisson-ish.
Edit: Seeing your added question, I don’t need an efficient estimator in the usual sense per se. This is more about how to search the parameter space in a reasonable way to find where the minimum is, despite the noise.
Hm. Is the noise magnitude comparable with features in your search space? In other words, can you ignore noise to get a fast lock on a promising section of the space and then start multiple sampling?
Simulated annealing that has been mentioned is a good approach but slow to the extent of being impractical for large search spaces.
Solutions to problems such as yours are rarely general and typically depend on the specifics of the problem—essentially it’s all about finding shortcuts.
The parameter space in this current problem is only two dimensional, so I can eyeball a plausible region, sample at a higher rate there, and iterate by hand. In another project, I had something with an very high dimensional parameter space, so I figured it’s time I learn more about these techniques.
Any resources you can recommend on this topic then? Is there a list of common shortcuts anywhere?
That rather depends on the particulars, for example, do you know (or have good reasons to assume) the characteristics of your noise?
Basically you have a noisy sample and want some kind of an efficient estimator, right?
Not really. In this particular case, I’m minimizing how long it takes a simulation reach one state, so the distribution ends up looking lognormal- or Poisson-ish.
Edit: Seeing your added question, I don’t need an efficient estimator in the usual sense per se. This is more about how to search the parameter space in a reasonable way to find where the minimum is, despite the noise.
Hm. Is the noise magnitude comparable with features in your search space? In other words, can you ignore noise to get a fast lock on a promising section of the space and then start multiple sampling?
Simulated annealing that has been mentioned is a good approach but slow to the extent of being impractical for large search spaces.
Solutions to problems such as yours are rarely general and typically depend on the specifics of the problem—essentially it’s all about finding shortcuts.
The parameter space in this current problem is only two dimensional, so I can eyeball a plausible region, sample at a higher rate there, and iterate by hand. In another project, I had something with an very high dimensional parameter space, so I figured it’s time I learn more about these techniques.
Any resources you can recommend on this topic then? Is there a list of common shortcuts anywhere?
Well, optimization (aka search in parameter space) is a large and popular topic. There are a LOT of papers and books about it.
And sorry, I don’t know of a list of common shortcuts. As I mentioned they really depend on the specifics of the problem.