[Q] Scheduler constraints on score progress

Do any of the flaml or ASHA schedulers make any assumptions about the score evolution curve across several iterations, e.g., regarding its monotoneity (or _monotonicity_, rather?)? I.e., does the score have to be ever increasing, or can it be decreasing as well for the early stopping algorithm to work properly?

I mean, one could adjust the design (or, rather the pre-/post-processing) of the scoring to respect this kind of constraint, e.g., by always accumulating to previous scores so that the score is always increasing from one iteration to the next (if the score for each iteration is positive), but I was curious whether or not this is required.