The fact that the more times you release differentially private estimates, the larger the accumulated privacy loss becomes is a common phenomenon in Differential Privacy and is generally attributed due to a very useful property in the differential privacy literature known as composition. Many of the well known differentially private algorithms rely on various composition theorems to actually limit the accumulated privacy loss. If you are interested, you can take a look at this paper : http://proceedings.mlr.press/v37/kairouz15.pdf 2 for more information on composition theorems.