Did you try a later kernel? out of the box ubuntu 16.04 is on the longterm 4.4 kernel. It looks like some ryzen features and patches have been added to 4.10, and they probably were not back-ported to the longterm kernels.
Not OP, but just built at Ryzen 1600 box. I've had _more_ instability when running 17.04 and settled on 16.04 which has been mostly fine, but hard crashes occasionally.
I custom built a machine last week for the first time in over a decade and from a fairly new processor and a just released video card. If I had more confidence in my PC building I guess I'd be more upset, but there are a lot of variables here and I'm still in a honeymoon phase.
I installed the official AMD RX580 drivers and it's been stable since.
Nothing out of the ordinary with a new platform. While Linux often takes longer to work this stuff out, Windows often has had similar issues in the past as well.
Having experienced first hand AMD driver instability on both Windows & Linux, AMD have lost my custom for the next 10 years..
Multiple re-occurring driver crashes using their main graphics card product line(RX380) on Windows 10..
So, pretty mainstream and yet having driver crashing (even when doing non-intensive tasks e.g. web browsing)
For the record, I'm not so sure Nvidia is any more stable either.
The only (constantly) stable graphics provider over the years has been Intel's on-board graphics.