Surely that reinforces my point? That what matters isn't the stopping rule but your evaluation budget? If you can afford 100 evaluations, do 100 evaluations. Pick any stopping rule based on the objective function and I can construct you a scenario that either has you spending a long time on the wrong side of it, or stopping prematurely. Might as well have predictable behavior.

I think that in the context that he meant, 64 variables = 64 hyperparameters because it was about benchmark problems solved in black-box settings. In other words, it is not about the common misconception of comparing #hyperparameters and #variables on some ML model, where the latter can be in 10^7.

You're correct -- I'm talking about how many variables control the behavior of the black box.