law enforcement sources tell TMZ, and we're told Gaga is offering $500,000 for the return of her dogs, "no questions asked.".

We don't know what was said, but the dog walker was shot and the gunman made off with 2 of the dogs, named Koji and Gustav.

There are reports there were only 2 Bulldogs being walked with one taken and one escaped that was later found, but our law enforcement sources tell us 3 dogs were being walked and 2 were taken by the gunman.