Puppy vomiting around 6 am 2-3 times a week--will he outgrow this?

My puppy is 16 weeks old. Just completed his vaccinations and has not been exposed to any questionable areas. For the last two weeks, the puppy has been vomiting approximately a teaspoon or less of a yellow-brownish liquid around 6 am (bile tinted with the shade of his food). I have discussed with my vet and he feels it is "empty stomach syndrome". On my vet's advice, I have been giving the puppy a snack at bed-time which is helping some. My vet hopes/thinks he will out grow this. Right now I am to monitor and report if the frequency increases. He is fine otherwise. Eats a healthy food he has done well on, has good elimination and is active and playful. Again, have discussed with the vet during his last 2 appointments. My question: has anyone experienced a puppy that vomits like this and did your puppy outgrow the vomiting? Would a probiotic help? I didn't ask the vet about that, but will. Thank you.