Installing and Using the Rolling LTS Kernel on Ubuntu 16.04
Ubuntu LTS releases used to pick up the newer MESA and kernel whenever the next regular release came out.
Apparently they’re switching things up now — you can install the Rolling LTS Enablement Stack to get the kernel from the latest stable Ubuntu release.
So basically, if you’re on 16.04 with the default 4.4 kernel, this gets you up to a supported 4.8 kernel.
There’s an official schedule: