In a study published by the journal Science, it was found that female budgies prefer intelligence in a mate.
In experiments, select males were trained to open a box containing treats. Other males were not. The females were able to choose between males who could open the treat boxes and males who could not. The females overwhelmingly chose the males who could solve the puzzle, even if they had previously been passed over as mates.

Actual mating was never observed – so it is not clear whether the new male were chosen by the females to mate with or were just to be friend zoned. You can read more about the study here.