How does Bayesian Optimization work when the objective function is binary?

[dli1]

If the objective function is binary, for example, the objective function is either relevance (1) or non-relevance (1), how does Bayesian Optimization work in this case?

See I have got the predictive mean (mu) and variance (sigma), here the range of mu is (-infinite, +infinite), not {0, 1}, is it reasonable to use mu and sigma to construct traditional acquisition function like EI, PI?

If not, suppose I turn the output of GP (mu and sigma) into a class probability using a link function ( e.g. 1/(1+exp(-mu)) ), then the new output and the original sigma are not in the same magnitude. In this case, how to construct acquisition function?

[apaleyes]

I think we have a model to support binary objectives implemented somewhere. Maybe it is worth publishing it as a notebook example. @javiergonzalezh thoughts?

[zjensen262]

Was this issue ever addressed? I am also interested in using this package with a binary objective function.