best_f vs current_value

[samuelkim16]

What is the difference in best_f used in acquisition functions such as qExpectedImprovement, and current_value used in acquisition functions such as qKnowledgeGradient?

[Balandat]

They're essentially the same in spirit / semantically. For analytic EI, best_f is indeed the best observed function value so far of the black box function f. But for the MC acquisition functions such as qEI and also qKG, we allow to pass in some generic objective function, so it's the best objective rather than the best function value in general. Arguably, one should probably rename the arg to qEI for consistency, but as it's the generalization of EI specifically this is done for historical reasons.

[samuelkim16]

Thank you! Is there a reason why this tutorial on Multi-Fidelity BO re-calculates the current_value in each iteration despite a separate objective function not being used (as far as I can tell)? Could one just keep track of the current_value?

[Balandat]

I am not sure I understand what you mean by "Could one just keep track of the current_value".

The current_value depends on all of the data observed so far, so you need to re-calculate it whenever you get new data. Note that there is an additional complication here with multi-fidelity methods in that we can't just optimize the posterior mean of the model across all parameters, but instead need to fix the target fidelity and optimize w.r.t. the other parameters - this is why FixedFeatureAcquisitionFunction is used here.

[samuelkim16]

Ah I think I misunderstood current value. This is the expected best function value, as opposed to best_f which is the observed best function value - is that right? Which is why it needs to be re-calculated in the case of knowledge gradient.