The lovey-dovey, practically inseparable couple headed out for some shopping Thursday afternoon with friends, and looked happy as ever as they snuck in a few pecks. Pete's right -- being engaged really is f***in' lit.

What's more interesting, though, are their outfit choices as they left their $16 million digs -- Pete went for some sort of sweatsuit incognito look ... equipped with shades and a face mask.

Ariana, on the other hand, couldn't have drawn more attention to herself -- or her rock -- by opting to complement her ripped jeans and chunky shoes by wearing just a bra for a top.