Rumer Willis -- Hollywood Hills Home Burglarized

Rumer Willis' Hollywood Hills home has been burglarized ... and the thieves made off with roughly $10,000 in stolen goods -- TMZ has learned.

Law enforcement sources tell TMZ ... Rumer's house is under construction and currently unoccupied. So far all cops know is that in the last 24 hours, someone entered through an outside gate ... slicing through a lock with a blow torch type device.

According to sources, the burglar entered the home and snatched up roughly $10,000 of the contractor's tools ... before taking off.

It's unclear if any of Rumer's personal belongings were also taken.