When changing the priority of a process, there is a warning about system instability.
I am running a Machine Learning algorithm and the Normal priority makes the computer unresponsive. Does changing the priority of this process cause problems or affect the process (besides making it run slower)?
No, it's just a warning. You probably aren't going to cause any problems by turning the priority of a process up or down a notch. And there won't be any irreversible damage; anything you do mess up can be fixed by a restart. Just make sure to save your work first before experimenting!
There are a couple of common things that can go wrong (and thus that you should watch out for):
You can crank up the priority of a non-system process so high that it can cause the system to become unstable and non-responsive because the system processes don't get enough time.
You can crank down the priority of a system process so low that it doesn't get enough time, causing your system to become unstable and non-responsive. (Although I think they've fixed some of this more recently by preventing you from altering the priority of certain so-called "critical" system processes.)
In my experience, assuming a decently fast and stable machine, as long as you stay away from the "Real Time" option, you will be fine. Turning non-system process down in priority level is even less likely to cause harm.