I can't find one in the dictionary.
There is a word "disimprove" so "disimprove on" is a catachresis waiting to happen. I think it would be easily understood. But I'm looking for an existing word.
The question presupposes an understanding of the difference between "improve" and "improve on." Here are two examples I feel are correct:
I want to improve my GPA.
I want to improve on my last year's GPA.
In both examples I am comparing my current GPA to my previous GPA. But "improve" is used for the thing being compared (current GPA) and "improve on" for the thing being compared to (previous GPA).
If the difference is between the subject of a comparison and the object of one, it seems to me that "improve" has multiple antonyms but "improve on" doesn't have even one.