Depends where your are, you can call the cops (record the loud music in case he turns it off and denies it before they arrive). Even if it is the weekend, loud music at 4 am is no excuse. R/legaladvice or r/prorevenge on reddit could be helpful too.

I'd record it and call the police. Here you have to turn music down after 11pm.

I think the only actual solution will eventually be to either kick out the roommate or to find a new place to live depending on who’s name is on the lease. Roommates are like siblings in some ways - You don’t want to escalate it to the police unless absolutely necessary because they are living with you and can make your life miserable if they want. I am a bit confused by “floor mate”. I was assuming it was a roommate situation - Sharing a common space with individual rooms to sleep in. If this is about separate apartments the situation is somewhat better, but you still have to be careful about involving the police as there will be no mystery about who called them and your neighbor knows where you live.

Apartment leases typically stipulate quiet hours. Check your lease. Even if there's no stipulation, you can call the police on them for disturbing the peace.