I'm using Apple Music on two devices: MBP and iPhone 5. Got the problem that iTunes doesn't automatically refresh the "For You" section on my MBP, unlike the iPhone. The CMD+R doesn't work as well. The only way to get fresh suggestions and playlists in "For You" is to kill and restart iTunes.
In iTunes, open the dropdown menu for your account (to the right of the apple logo at the top of the screen) and select "Choose Artists for You."
On the next screen (floating bubbles of "what you are into"), hit "next" without making any changes.
On the next screen (floating bubbles of "your favorites"), hit done.
On my Mac, this refreshes the "for you" every time. Pressing the "new" button as suggested by others has no effect on my Mac.