To regret one's decision :از تصميم خود پشيمان شدن
To go back on one's decision: از تصميم خود صرف نظر كردن
Regretting a decision means it already has happened, and you wish you hadn't done it.
Ex: I regretted my decision to throw away my old sunglasses . It means :I threw away my old sunglasses, but I wish I didn't.
To go back on a decision would be like thinking of doing something, but then not doing it at all.
Ex: I went back on my decision to throw away my old sunglasses ,just in case.it means: I almost threw away my old sunglasses, but then decided I would need them later.