Demi Lovato Starts 'Sorry Not Sorry' House Party Tour with Rob Gronkowski in Boston

Demi Lovato had a great idea for a mini tour to promote her new song -- house parties featuring local celebs ... which she kicked off in Boston with Rob Gronkowski.

Demi hosted a rager Tuesday at a pad she rented in Beantown, which was stop #1 in her "Sorry Not Sorry" House Party Tour ... which is exactly what it sounds like.

Sources close to the singer tell TMZ she came up with the idea at a recent house party ... wanting to offer fans an intimate setting to enjoy her new single, "Sorry Not Sorry." As for how Rob got involved ... we're told she wanted to invite a hometown hero ... and he happily obliged.

Demi hosted about 200 guests from the area, and ended up doing 3 songs, including "Sorry Not Sorry" ... naturally.

TMZ broke the story ... Demi's L.A. home was hit in a possible burglary attempt. We're told she's aware of what happened, but pressing on with the house party tour. She'll do 2 stops, in Birmingham and Nashville on Wednesday ... then it's off to Vegas, Austin and Dallas.