Explain your feelings to the neighbor ... always best to give them the chance to control the dogs before you do anything ... if that doesn't work, then maybe take other action.
I agree that you need to talk to your neighbor FIRST.
Nothing will PO a new neighbor quicker than going to the dog warden/police before you even speak to him.
I had a similar situation at my place, only it was MY dogs getting out. I have a invisible fence. I am obviously NOT home and monitering them 24/7. But when we are home, they are house dogs. They were always there waiting on the step whenever I get home, wether it be from work, or jst a quick trip to the store. I honestly didn't know they were getting out until a visit from the game warden because a neighbor called on us. It kinda puts a bad taste in your mouth if ya know what I mean. I would have much perfered they just came an talked to me.
As it turned out, there collars both didn't work. They were charging, and the LED indicated they were good, but NO shock. I promptly got new collars ordered the next day. Problem solved.
Now I understand this guy probabally KNOWS his dogs are getting out, but if it is just a once in a blue moon thing, he may not realize how bad it bothers you.
So certainly talk to him first. He may turn out to be the best neighbor you can ask for. But if the warden/cops show up at his house because you called on his dogs, well then I doubt he will ever be a good neighbor.