The leaves can be eaten raw or cooked. It may take a while to adjust to the taste, but free food is free food, right?
If you can get to an Asian market and buy one of their fresh sweet potatoes (or what ever they may call it) that type may have better tasting leaves.
Or look for 'Japanese Sweet Potato with Edible Leaves' and you may find the exact kind they use in Japan.
I have been nursing a few along inside the house this winter hoping they can hang on until the weather warms up.
Edited to add:
Sand Hill has tons of varieties; some in limited quantity.
http://www.sandhillpreservatio...
The one I was thinking of may be called Okinawa or Okinawan by some sellers.