[FEATURE REQUEST]: qConstrainedExpectedImprovement

[JanRotti]

Motivation

Hello,

I was wondering if there is any way to combine the qExpectedImprovement and ConstrainedExpectedImprovement.

I see that it is possible to use constraints in qExpectedImprovement, but it does not use it in the form of a probability of feasibility (atleast I dont think so).

Best regards,
Jan

Describe the solution you'd like to see implemented in BoTorch.

qConstrainedExpectedImprovement with similar signature as ConstrainedExpectedImprovement

Describe any alternatives you've considered to the above solution.

Usage of qExpectedImprovement in the probability sense of the feasibility.

Is this related to an existing issue in BoTorch or another repository? If so please include links to those Issues here.

No response

Pull Request

Yes

Code of Conduct

• I agree to follow BoTorch's Code of Conduct

[SebastianAment]

Hi @JanRotti, thanks for reaching out.

I see that it is possible to use constraints in qExpectedImprovement, but it does not use it in the form of a probability of feasibility (atleast I dont think so).

qEI computes the probability of feasibility by averaging over the feasibility indicator per sample, i.e.

CEI(x) = E_{f,c}[improvement(f(x)) * feasibility(c(x))] 
       ~ mean_i improvement(f_i(x)) * feasibility(c_i(x)),

where f(x) c(x) are random variables corresponding to the objective f and a constraint c evaluated at x. f_i(x), c_i(x) are specific samples of f(x), c(x) used in the Monte Carlo approximation.

If we make the simplifying assumption that f and c are independent,

CEI(x) = E_{f,c}[improvement[f(x)] * feasibility(c(x))] 
       = E_{f}[improvement(f(x))] * E_{c}[feasibility(c(x))]
       =  EI(x) * probability_of_feasibility(x)

So qEI contains the probability_of_feasibility as a factor if the objective and the constraints are statistically independent. In contrast to ConstrainedExpectedImprovement, qEI also allows for dependent constraints, in addition to non-Gaussian objectives and constraints.

Note that ConstrainedExpectedImprovement uses GPs to define the constraints as well. If you have a probability of feasibility model that is not related to a GP, you can check out the feature added in @jduerholt's PR here, which adds support for external probability of feasibility models.

Last, we strongly recommend using variants of the LogEI family of acquisition functions. In this case either qLogExpectedImprovement or LogConstrainedExpectedImprovements. These have much better optimization performance, especially for constrained problems. See our NeurIPS article or this talk for details.

Let me know if you have questions about this.