Potato help

Hi, I'm going out of town for 2 weeks as of Friday, and have 3 containers of potatoes. I have never had potatoes succeed, and want to know if I should be pulling them right now, or if they will survive 2 weeks of only nature watering (you know, 3 -5 drops a day,) and if they are ok if they are not immediately pulled after the tops die back? We're also supposed to have our 1st frost date when I am gone, and idk if that will affect them either. I'd rather have a few small potatoes than come home and find mush. Thank you!