Dogs are creatures of habit...good and bad. Your dog has trained you to let it out at 4 am. He has become the Alpha member of his pack. He is letting you know he is ready for his day to start. Now ithas become a habit, which is turning into a behavior issue.
Odds are, he really doesn't need to relieve himself because he has gone out 3 times since dinner. Most likely he's just checking things out in his back yard. All kinds of neat stuff crawl and prowl around backyards at night.
Problem is, it looks like you're not having as much fun investigating as he is!
If you don't want to get up to let him out at that hour, crate him at night. It won't take long for him to realize his "demand" for going out at 4 is ignored by the Alpha members of his pack, (that's you!) and he will eventually settle down and wait until you get up. The good thing is, the majority of dogs that are crated, won't soil in their crate, if it's the right size for them.
If you want your dog to develop habits...make them good ones!
Being a dog is fun! Being a GOOD DOG! is even better!