Enforce the constaint "x1*x2=32"

[aleczhanshi]

Hi there, following the last issue, is there a convenient way to have a constraint like "x1*x2=32" using the outcome variable or "metric"? In particular, I want to add this to https://github.com/pytorch/botorch/blob/master/tutorials/custom_botorch_model_in_ax.ipynb and need a strict equal instead of GEQ or LEQ. Thanks!

[Balandat]

Can you just re-parameterize things on your end then?

Like get rid of x2 and only optimize over x1, then in your evaluation you just plug in x2 = 32 / x1? Or is your idea to model things across the whole domain (b/c you have data and want to use it) but put the constraint on only for the optimization?

[aleczhanshi]

@Balandat Hmm, I kinda simplified it so this won't work in my problem. My problem is more like an optimization of f(x1, x2, x3, x4, x5, x6 ..., xn) where x1*x2*x3=32, x4*x5*x6=32, x1+x4<=8. Without specifying these constraints explicitly, the algorithm cannot even find a valid set of parameters. Is there any way that I can enforce this set of constraints?

[aleczhanshi]

@Balandat Hi there, I'm following up to see if there's any update on this thread. Thanks!

[Balandat]

Unfortunately, that setup isn't something we can easily support on the Ax frontend. In principle, you could specify these constraints for the optimization algorithm algorithm when generating new candidates, but that would have to happen on the lower level in botorch, essentially by passing the constraint according to scipy convention here: https://github.com/pytorch/botorch/blob/master/botorch/gen.py#L120-L128

This probably works ok if you have a decent model. My concern is that if you use this to generate candidates then your data will live on some lower-dimensional manifold defined by your constraints, and as a result my suspicion is that the model will have a very hard time getting reasonable fits.

I think doing this properly will require more sophisticated methods than we currently support.

[lena-kashtelyan]

This issue is a duplicate of #153, closing.