Googler here. Yes, in my team we have a colleague that is spending one day a week trying to solve a particular problem we have with a completely novel approach.

Googler here. Yes, in my team we have a colleague that is spending one day a week trying to solve a particular problem we have with a completely novel approach. He had an idea after we presented what we are up to in one of our Org summit. Furthermore, it is really a streamlined process, ie you only need your manager approval.