Request for documentation: example with `DeterministicModel`

[Kh-im]

Hi,

I'm trying to find the best strategy to a particular optimization problem. I have a scalar objective function to minimize f(x,y). x and y are both range parameters. The function is completely monotonous with a single global minimum so the solution is pretty obvious. But I have several outcome constraints. Do you have some recommended strategy for that ?

Thanks

[Balandat]

How long does it take to evaluate f? Is f "black box" or do you have an analytical form?

[Kh-im]

f is a black box but not very complex as we know some of the structure (like monotocity) but take a long time to evaluate (several hours for each eval)

[Balandat]

@bletham has worked on monotonic GP models in the past, seems like this would be useful here. Also, depending on how much you know about the structure of the function, it could be beneficial to define a custom covariance function.

How many outcome constraints are there?

[Kh-im]

Thanks for your answer. 10 constraints.

[Kh-im]

@Balandat to answer to one of your first question, let's say we have an anaytical form (x²+y²) for example to minimize. But we don't know the analytical forms of the outcome constraints. How can we exploit this knowledge ?

[Balandat]

Sorry for the much delayed reply. We have the notion of a DeterministicModel that you should be able to just use here by implementing the x^2+y^2 function (the most straightforward way to do this is via a GenericDeterministicModel.

Then you can stick this plus the models for the outcome constraints into a ModelList and use that us usual. That way you don't actually have to learn a GP model for a function that you already know.

Just to be clear though, when you evaluate a configuration, you do observe a value for each of the constrained outcomes (and then have a bound to check if each of those is feasible or not), right?

[Kh-im]

Ok, I will try that. Do you have any example using Deterministicmodel ?

yes ( for your question).
Thanks again

[lena-kashtelyan]

We don't currently have such examples, unfortunately, but we plan on open-sourcing code for a method that will provide a really strong example for using deterministic models sometime in 2023. Until then, the tutorial on using a custom model might be the most helpful, especially in conjunction with @Balandat's comment on how to construct the model as a ModelList (thank you @esantorella for the suggestion!).

Assigning this to @qingfeng10 who will be open-sourcing the method-in-question, so she can link the example here at that time.

[sgbaird]

Xref #935

[lena-kashtelyan]

Since it will unfortunately likely be a bit before we provide this, putting this on wishlist for now.