Lower Confidence Bound

[nikitrian]

Hello,

I have a minimization problem and I would like to use Lower Confidence Bound as the acquisition function. I see that Upper Confidence Bound is available in Botorch. If I set maximize=False in UCB (e.g acquisition = UpperConfidenceBound(gp, beta=10, maximize=False), would that give me the LCB? Or do I need to specify a custom acquisition function for LCB?

[saitcakmak]

Hi @nikitrian. Setting maximize=False will give you the negated LCB, i.e., it will return - mean + beta * std (see https://github.com/pytorch/botorch/blob/main/botorch/acquisition/analytic.py#L336-L339). If you then maximize this, e.g., using optimize_acqf, the candidate you get would be the point minimizing the LCB.

[nikitrian]

Thanks for your reply @saitcakmak. This makes sense, but I am not sure how to implement the maximization you are mentioning.

    candidate = optimize_acqf(
        acquisition, bounds=bounds, q=q, num_restarts=50, raw_samples=1024,
    )

This is how I optimize my acquisition function. Is there a way to set this to maximization?
and this is how I set the acquisition function:

acquisition = lambda gp: UpperConfidenceBound(gp, beta=1000, maximize=False)

[saitcakmak]

optimize_acqf will maximize the given acquisition function, so that part seems correct to me.

acquisition = lambda gp: UpperConfidenceBound(gp, beta=1000, maximize=False)

This pattern looks a bit odd to me. This will make acquisition require a GP as input, which would not work in optimize_acqf. Why not use acquisition = UpperConfidenceBound(gp, beta=1000, maximize=False) or something like

def get_acqf(gp):
    return UpperConfidenceBound(gp, beta=1000, maximize=False)

acquisition = get_acqf(gp)

You'll want the acquisition input to optimize_acqf to be an AcquisitionFunction (UpperConfidenceBound in this case) object.

[nikitrian]

@saitcakmak thanks a lot for your help. The implementation I have works well with expected improvement and I don't have any issues. The lower confidence bound seems to be working now as well.