Constraints on model prediction?

[samuelkim16]

Is there a way to place constraints on the model prediction? This is helpful in the case where I know the bound(s) or even the optimal value of my fitness function, akin to this paper: Knowing The What But Not The Where in Bayesian Optimization. The paper formulates a new GP assuming you know the optimal value ahead of time, although I would have figured that there is a simpler method of just clipping the model predictions when optimizing over the acquisition function.

As a side note, I thought this would be addressed by Outcome Constraints, although the example looks like it places constraints on the input rather than the prediction.

[esantorella]

BoTorch doesn't currently provide a way to do this out of the box.

You could probably hack this into an MCAcquisitionFunction (e.g. qLogExpectedImprovement) by clipping the samples drawn from the model's posterior, by modifying the posterior's rsample method. I find that approach a little weird since you're modifying the model only for acquisition function optimization and not when fitting it, but it might work.

Another approach would be to give the model an OutcomeTransform that can only produce values in some range. For example, the Log outcome transform provided in BoTorch makes positive predictions. Or you could easily define a log(y - f^* + small_number) outcome transform if you know the upper bound. That approach would magnify distances close to the optimum, which could be either good or bad for model fit. I think the paper is taking a similar transform-based modeling approach but with a different transform, although I don't understand exactly what it is doing.

Yet another modeling approach would be to modify the likelihood to e.g. a BernoulliLikelihood (if you knew outcomes were between 0 and 1), but then some nice analytic properties would be lost and model-fitting would be more difficult.

Outcome constraints denote which outcomes are unacceptable rather than impossible.

[Balandat]

IIUC this would entail defining a model that does not have a MVN posterior but a truncated MVN? If this truncation is via linear inequalities this would amount to a SkewGP model https://link.springer.com/article/10.1007/s10994-021-06039-x - we have an implementation of these in our internal code base but haven't had a chance to open source these yet.

[samuelkim16]

Thank you for the response. I found a more recent paper, Respecting the limit:Bayesian optimization with a bound on the optimal value on this topic. It looks like just clipping the acquisition function without modifying the model (labeled "TEI") performs about as equally as the original expected improvement (EI). The log transform idea looks similar (if not equivalent) to the SlogGP used in this paper (labeled as "BABO Fixed ζ"), which outperforms EI and TEI. (Of course, their own method, "BABO", appears to outperform all the other methods).

I will look into modifying the model using OutcomeTransform, as this seems like a good balance of simplicity and promising performance. Can I just apply the typical acquisition functions, or do I need to have some transform on these as well?

[Balandat]

I don't think you'd need any special treatment of the acquisition function(s) if you use an outcome transform. .