Question: SEBO optimization with parameter dependency | logistic parameter constrains about ax

[Balandat]

So what you're looking at is a hierarchical search space. We have some (basic) support for this (

Ax/ax/core/parameter.py

Lines 515 to 516 in fcc5178

	dependents: Optional mapping for parameters in hierarchical search
	spaces; format is { value -> list of dependent parameter names }.

,

Ax/ax/core/search_space.py

Line 437 in fcc5178

class HierarchicalSearchSpace(SearchSpace):

), but I'm not sure how such a setup would interact with SEBO.

@saitcakmak, @dme65 do you have a sense of this?

[saitcakmak]

I don't know how well HSS would interact with SEBO for this use case. Under the hood, the acquisition function will be optimized in the flattened space without fixing the values of x2 & x3, so these will be included in the sparsity computations as well.

Since the conditional structure here is super simple, you could try a manual approach here. Let Ax generate a candidate with all three parameters optimized and compare the acquisition value of this candidate to x1=x2=x3=0. You can then evaluate the one that performs better. But this would not scale too well beyond a few parameters. You could also do similar things using the fixed_features argument, which would let you fix x2=x3=0 and optimize x1 alone while generating the candidate.

Fixed features: https://github.com/facebook/Ax/blob/main/ax/modelbridge/base.py#L753-L755
Checking acquisition value: https://github.com/facebook/Ax/blob/main/ax/modelbridge/torch.py#L463

[dme65]

Assuming the target_point in SEBO is 0, this isn't going to work out of the box. The main issue is that x1=0 implies x2=x3=0 needs to be incorporated into the sparsity objective (penalty) and we don't expose any easy ways of doing that.

Your best bet is probably to find a way to optimize the acquisition function for each path in the hierarchical search space structure and then pick the best (this is what @saitcakmak suggested above). One thing to watch out for in that setting is that you may end up with x1=0 but not x2=x3=0 in the case where you optimize all parameters.

[yitingz]

@dme65 @saitcakmak @Balandat Thank you so much for your helpful inputs. When I use SEBO to optimize all parameters, it works well for most of the time and sometimes may have results with x1 = 0 but not x2 = x3 = 0. (main issue remaining for my problem) I will try to study more on this.